The only thing I was able to get from them was that case law was based
on public opinion
That is inaccurate. Case law is not based on public opinion. Case law is released by judges from appellate and supreme courts of a jurisdiction (be it state or federal).
The public, in the form of jury, might determine the outcome of a case in trial court by acting as fact-finders, provided that:
- the parties request reliance on jury (which is strongly suggested,
even if that may not always suffice to overcome the trafficking of influences between
judges and law firms);
- jurors follow the judge's instructions on how to evaluate evidence;
- the judge does not override the jury's findings; and
- the jury's findings/verdict (with the consequent judge's decision) is not reversed by an upper court.
That being said, the public/jury does not produce case law. The jury in one case does not influence how subsequent cases will be decided, let alone how or which laws will be interpreted in that case or anywhere else.
If anything, public opinion might have greater influence on civil law from the standpoint that voters directly elect who they want in Congress (whose job is to enact, amend, and repeal statutes, as you correctly point out later).
By contrast, judges in federal courts and in the states' appellate & supreme courts are appointed by the president or governor, accordingly. And even though judges in states' trial court are supposedly elected by public vote, the reality is that voters hardly ever participate in judicial elections, thereby allowing the aforementioned trafficking of influences to determine who makes it to judicial office.
Many state trial judges are able to stay in judicial office for several years because no attorney dares to contend against them. And that happens because lawyers are afraid that the judge will retaliate, thereby forcing the lawyer(s) to relocate his practice. This interesting article broadly reveals the shameless dynamics of a county trial court. Here I discuss more specific instances of judicial corruption, such as felon Carol Kuhnke, the judge who got in 2016 got busted with illegal narcotics; and former Michigan "Justice" Joan Larsen, who sided with the judge who terrorized, extorted and jailed three innocent kids.
Thus, also from this perspective it is evident that the people's chances to influence case law are very close to zero.
courts cannot rewrite the laws. That's congress's job. They can only
interpret the laws.
That's correct. The legalese for this contrast are the Latin terms (Congress') jus dare and (courts') jus dire.
Beware, though, that many judges deliberately violate that principle. Instead, they oftentimes engage in suppressing the legislature as well as case law so as to force unlawful outcomes.
Can a real-life situation be used to describe the difference between
common and civil law?
Yes. I covered that here. Although that answer has received many down votes, it provides verifiable sources and links to:
- case law stating that the legislature supersedes its common-law counterpart where statutory language is specific enough;
- a real-life case (which I litigated) where the legislature's specificity supersedes its common-law counterpart; and
- how the judges have been ignoring that legislation, babbling instead a common-law doctrine that contains gaps in one or more of its elements.