At least in the United States practicing lawyers are called to serve on juries. But my understanding is at least one side will always remove them before trial. Why would it always be the case that at least one side would not want someone with legal training on a jury?
Technically anyone can sit on a jury. Lawyers are not automatically excluded from juries anymore, as being called for jury duty is a right and a duty that the law abhors automatically excluding people from. That is the official line on this. However, in reality, lawyers will always be stricken from serving by one of the lawyers trying the case. Each lawyer has a certain number of preemptory strikes (the ability to get rid of a juror for any reason, aside from those protected by law, such as race, religion, etc). They also have unlimited "for cause strikes," which are when a juror is biased in some way.
Lawyers trying the case almost always try to use a cause strike to get a lawyer off, saying that they are biased toward either Defense or Plaintiffs based on the type of law they practice. The judge will usually not let them use a cause strike, saying that an attorney is ethical enough to apply the facts to the law and not sway the jury based on their personal biases that everyone has; plus, we're officers of the court so we have a duty to be ethical. Hence, they are typically forced to use a preemptory strike to get a lawyer off, but they will, every time. (If the lawyer just tried a similar case, then they'd get to use for cause.)
The real reason that the lawyer from one side or the other definitely wants a lawyer off is that the jury instructions presented by each side to the judge are crafted in a way that each word carries specific meaning and, with that, is designed to lead to a certain way of thinking. Once the lawyers have fought over the instructions and the judge decides what will be presented, the jury only gets them in writing...in some states not even in writing, they only get them read to them without a copy to take back to the room.
If a lawyer is in the jury, that person will undoubtedly be able to explain exactly what the law requires for a finding, or exactly why a certain finding should be had. They will advocate one way or another; this is undeniable. The instructions are purposefully confusing. The reason is this: when we fight over jury instruction, inherently, one of us will want an instruction that is hard to understand, for a lay person. This is because we want them to apply the law as it is commonly (mis)understood, not as it truly is, because that's not good for our case.
To have a lawyer on the jury would defeat the finely crafted instruction and its potential to confuse. They would undoubtedly explain the instruction to the jury. One may think this would be helpful, however, juries are told that any special knowledge they have about anything pertaining to the case shall not be shared as it could sway the jury. This is most true when it comes to a lawyer sitting. When a jury doesn't understand a jury instruction, their only recourse is to send a question to the judge. In states where they have the instruction in writing, all he can say is "read carefully;" he cannot give his interpretation of what the instruction means. If a judge did give his own interpretation that is grounds for a mistrial or an appeal at least. A lawyer on the jury would be able to explain, "Oh, what this really means is X," and this is bad from one side's perspective, almost always. We all have biases, and even finely determined rules of law can be subtly pushed toward one direction or another with the use of a certain word over another, or the placement of one element before another.
Generally, unless the side who would most want the attorney off had exhausted their preemptory strikes, and lost the argument to remove for cause, there is very little chance a lawyer will serve. The fact of the matter is that both sides are very likely to want a lawyer stricken from the jury pool, (even from the side who may believe the lawyer to have leanings in their favor). It is essential to control as many factors as possible in a jury trial, and an attorney on the panel is just a wild card. The potential always exists that if a lawyer ends up on the jury, they could explain the elements of the case to their fellow jurors, who may then not rely as fully upon the carefully crafted language in the instruction(s). This could backfire on either side when certain portions of the language used may be intentionally vague or difficult to parse though for someone who doesn't practice law.
Anyone interested in the process of choosing and striking jurors (in the U.S.), through the process of voir dire, this is a fairly comprehensive article on the topic.
@AdamZerner Even in situations where both attorneys generally believe the law is in their favor, it is likely that both parties would strike attorneys during voir dire. As mentioned above, attorneys are too much of a wildcard. Depending on the type of law they practice, the clients they've dealt with recently, and the specific cases they've had throughout their career all would play a huge role in how the attorney in the box would view the case. For example, an attorney who has worked as a criminal defense attorney their entire life will naturally view the case from a defensive perspective. A products liability plaintiff's attorney will naturally be skeptical of the manufacturer in a products liability case. While this is true of every profession (every juror brings their own biases and experiences into the box), the difference with attorneys is the risk that jurors will give the attorney's opinion significantly more weight than they give another jurors opinion or even their own opinion. It's much safer, even when you believe the law is on your side, to strike attorneys.
Additionally, I too would be interested in seeing some stats on how frequently the side who used a preemptory strike on a lawyer ended up winning. That said, I don't believe there would be a strong correlation between striking an attorney and losing or winning the case since nearly every trial attorney believes in striking other attorneys during voir dire.
And finally, to your hypothetical about both sides genuinely believing the law is in their favor, I would say it's rarely as simple as you make it seem. While attorneys may believe the black letter law is in their favor, the way that law is interpreted and applied to certain situations is determined by case law. The tough part about case law is that both sides can almost always find cases with decisions that support their argument. That being said, they will also find the cases with decisions that counter their argument. One of the fun parts of being a lawyer (yet also one of the most challenging parts) is sorting through all of these decisions, analyzing what facts made the cases come out different, and crafting an argument to suggest the black letter law should be interpreted in your favor. This process is more public during bench trials and at the appellate level (because at that point you're making your arguments to judges), but all of this is still done behind the scenes by lawyers when preparing for a jury trial. After doing all of this research and preparation for trial it is very often the case that each attorney believes their side should win. Let's not forget that only 2-4% of civil cases make it to trial and about 8-10% of criminal cases make it to trial. So in reality, most cases that make it to trial get there because they are the "close calls." When it's truly a cut-and-dry case, it's almost guaranteed it will never get before a jury. The few cases like that which do make it to a jury only make it that far because one party's client is too stubborn or prideful to concede to a settlement.