Utah and 8 other US States have different ages of consent for each gender. Why is this?
This is more a question about society and politics than about the law; that is, you know what the law is you want to know why.
Without any research and no idea of the particulars I can say that the reason is historical and derives from the fact that our society has been (and still is) a patriarchy and has deeply ingrained sexism (along with a lot of other -isms). These laws were laid down when it was considered not only acceptable but prudent and reasonable to treat men and women differently and nobody has got around to changing them.
That said, they are quite likely unconstitutional as discrimination on the basis of sex is unlawful. For why they are still there see Why do municipalities keep laws on the books that are invalid? - it is equally applicable to states; I would suggest my idea No 1.
Women can get pregnant, so men can be held to stricter rules:
Although legislation tends to reflect general societal attitudes regarding male versus female ages of consent, Richard Posner notes in his Guide to America's Sex Laws:
The U.S. Supreme Court has held that stricter rules for males do not violate the equal protection clause of the Constitution, on the theory that men lack the disincentives (associated with pregnancy) that women have, to engage in sexual activity, and the law may thus provide men with those disincentives in the form of criminal sanctions.
Posner, Richard (1996). A Guide to America's Sex Laws. The University of Chicago Press. p. 45. ISBN 0-226-67564-5. The case cited is Michael M. v. Superior Court, 450 U.S. 464 (1981).
However, to modern sensibilities, this doesn't justify the states that have age of consent lower for women. [The pregnancy argument would mean states could punish an adult male for sex with a minor female, to protect the woman. Whereas a minor male of that same age doesn't necessarily need the same protection, at least for that concern.]
Law in those states seems to be an attempt to mirror the historical tendency for men to be slightly older than women when marry - but re goal of discouraging sexual predation, those states have it backwards.
I'd have to agree with the answers that speculate this is a patriarchal holdover that eventually will change or be overturned. [But US Supreme Court - having ruled it isn't inherently an Equal Protection violation - seems inclined to leave these laws alone regardless of which age is slightly lower; leaving it to the states to decide the non-symmetric circumstances of the sexes.]
More detail from the case itself:
(a) Gender-based classifications are not "inherently suspect" so as to be subject to so-called "strict scrutiny," but will be upheld if they bear a "fair and substantial relationship" to legitimate state ends. Reed v. Reed, 404 U. S. 71. Because the Equal Protection Clause does not "demand that a statute necessarily apply equally to all persons" or require "things which are different in fact . . . to be treated in law as though they were the same," Rinaldi v. Yeager, 384 U. S. 305, 384 U. S. 309, a statute will be upheld where the gender classification is not invidious, but rather realistically reflects the fact that the sexes are not similarly situated in certain circumstances. Pp. 450 U. S. 468-469.
The Equal Protection clause of the 14th amendment provides for equal protection under the laws.
The Supreme Court has held this prohibits sex based discrimination, unless the government proves this law satisfies the intermediate scrutiny test.
In brief, this test means: the law furthers an important government interest in a way that is substantially related to that interest.
This standard was applied in Craig v. Boren (1976). In this case: "Oklahoma passed a statute prohibiting the sale of 'nonintoxicating' 3.2% beer to males under the age of 21 but allowed females over the age of 18 to purchase it. The statute was challenged as Fourteenth Amendment Equal Protection violation by Curtis Craig, a male who was over 18 but under 21, and by an Oklahoma vendor of alcohol." In this case the Supreme Court "held that the gender classifications made by the Oklahoma statute were unconstitutional because the statistics relied on by the state were insufficient to show a substantial relationship between the statute and the benefits intended to stem from it."
For more see: https://en.wikipedia.org/wiki/Craig_v._Boren
In this day and age, it is unlikely that different age of consent laws would be upheld. The only problem is that you must have standing to challenge such laws. As minors cannot file lawsuits, without their parents, the most likely case providing standing would be where someone knowingly violates the law and is arrested for violating it. Then the person would have legal standing to challenge the age of consent laws. But that requires a lot of effort, could result in you spending some time in jail while the case is appealed and so forth.
Even more likely, the differences in age of consent will not be enforced by the government, leading a situation, where the law is on the books, and has not been ruled invalid, yet is most likely unconstitutional.
TL;DR: So in the end, the ages are practically not different, and just historically exist on the books as different.
Edit: as pointed out by ToolmakerSteve, (Thanks!) there actually is caselaw on this issue: Michael M. v. Superior Court, 450 U.S. 464 (1981). It was a plurality opinion and it seems to be quite a persuasive authority on this issue. In the current composition of the Supreme Court staggered age of consent laws by gender would probably continue to be upheld; when I first wrote this answer Justice Kennedy was still a Supreme Court justice and his expansive view of the equal protection clause seemed to swing such a case the other way.