When debating a topic such as the origin of gender-specific toy preference, discussions such as the following are common:
A: Studies show that small children typically choose toys associated with their gender, girls prefer dolls and boys prefer trucks and so forth.This is a reasonable interaction, but there is in fact a flawed premise in B's response, which A then accepts as valid. Beginning in A's first statement, we are talking about small children, and then parents are introduced in B's response. Implicitly, B is viewing the child as the subject of an experiment: If the child prefers gender-specific toys because of socialization, then that behavior may not be innate. A then responds that if the child exhibits that preference before significant socialization, then it may well be innate. In both cases, the child's behavior is what is being investigated, and is what teaches us about the innateness or non-innateness of the behavior in question.
B: Sure, but that does not mean it is "natural" for them to do so - it could be cultural, in that their parents and peers encouraged them towards that behavior.
A: Fair enough. However, some studies have shown such preferences in children too young to have had much interaction with society, which would support the assertion that such behavior is at least in part innate.
But that perspective is flawed, for the following reason: We have no reason to exclude the parents from being the subjects of investigation as well. It is theoretically possible, for example, that there is not an innate tendency for children to prefer gender-specific toys, but that there is an innate tendency for parents to direct their children to gender-specific toys. If we accept that evolution affects behavior, then it does not just affect child behavior but also adult behavior.
Of course the adults have been heavily integrated into society, making it very hard to know whether such a behavior on their part - if they in fact exhibit it - is innate or not. For that reason it is natural to focus on the child, which is closer to a "controlled" experiment. However, the difficulty of investigating a fact does not affect whether it is true or not.
That parents (or peers) influence children to prefer gender-specific toys is evidence that that behavior is not entirely innate on the part of children. However, it does not rule out that in the human species as a whole, such behavior may be said to be innate - it may not be "directly" innate, but then few traits are, as genes can act through cascades of many levels of biological effects. For example, if it improved the fitness of our ancestors to have children prefer gender-specific toys, then causing them to do so could have been achieved in various ways - genes affecting the children, genes affecting parenting behavior, and so forth. Either, both, or none might have occurred and been selected for. But the point is that there is no reason to assume it must be a gene directly affecting the child's behavior - evolution does not care about the means so long as the end result is beneficial.
In conclusion, this might appear like an argument saying it is impossible to prove that gender-specific toy preference is due to cultural factors, since even if it is shown that children do not spontaneously exhibit such behaviors, we must now consider the possibility that other innate factors in the human species cause them to do so. As such, this might seem to verge close to making it impossible to show that a behavior is not innate, which is a dubious position. However, of course such an argument is not evidence that the behavior is innate - just that an important level of complexity must not be ignored here.