A false premise fallacy is when an incorrect or logically unsound premise forms the base of an argument- whether or not the CONCLUSION drawn from that argument is in fact true.
Unfortunately having a sound conclusion from false premises can make it harder to refute those false premises, because the conclusion drawn from them is correct.
Premise 1: Evolution is change in organisms over time.
Premise 2: We can watch a child grow and change over time.
Conclusion: Evolution is true.
While the conclusion here is in fact true- evolution is a scientific fact- the premises are both shoddy. Evolution discusses populations not individuals, and discusses gene distributions in those populations not the change and growth in a regular individual. Therefore you now have an argument where the conclusion is sound but the arguments advanced for that conclusion are flawed.
People tend to practice "pile up arguing" where people will throw out any and all points towards the position they want to promote. They will not think about what other positions they would have to support in order to be consistent with their reasoning or even the incidental effects their argument may have on other people's opinions other than pushing the conclusion they want others to accept.
A good example, people often respond to pro-lifers saying that "it's not a person because it's not legally defined as a person" or "murder is when the law prohibits killing". This skirts the issue and if you really think that line of reasoning is sufficient to support the pro-choice position then to be consistent if the government changed its mind or even if the government decided for example to set the age of personhood (and the right to life) at 50 then you'd have to just go along with it.
Now the pro-choice position may be the right position (I'm not saying which for the purposes of this post), but that doesn't make any and all arguments advanced in its favor right. A position can be right but some of the arguments used to advance it can be flawed.
People rarely ever call people out on their reasoning when they agree with the position they are supporting, but it must be done if we are going to be intellectually honest.
Another good example is "homosexuality can't be a choice because why would you choose to be gay and get hated." A disproving example (for this line of reasoning, not for the notion that homosexuality is not a choice, again I'm not taking a position on this issue within this post) is Jewish people and other religious minorities throughout history continuing to practice their religion even in the midst of strong social pressure not to.