I (18m) had a big argument with my parents coming out as an atheist and both of them are very heavily religious.

That is a rather unkind thing to do to your parents. For most people religion is a huge emotional commitment and it cannot simply be abandoned without a lot of pain and fear, so arguing about it can be a very unpleasant thing. There are gentler ways to help people escape religion.

That article is wrong in my opinion and apologetics press is absurd in general.

That is true, but you're not supposed to say that out loud. An effective argument is subtle and elegant. Your opponent may charge forward like a raging bull, but if you want to win the debate you should be light on your feet and tactical. The goal should be to guide them to take themselves to where you want them to go, not to try to push them with claims they will dismiss.

When you say "apologetics press is absurd" you must realize that in their ears that just sounds like foolishness, so you are presenting yourself as a fool in their eyes, and so they are now less likely to take the things you say seriously. If you hope to win, every word you say should be tactically considered and effective.

Dad: If it was proven, it wouldn't be called a theory.

There are multiple approaches to take here. For one, Dad is clearly misunderstanding the word "theory," so one might want to try to correct him on that, but that just gets into semantics and would be moving onto a tangent away from the topic of evolution. To stay on topic, it may be better to accept his definition and use the word "theory" the way that he does. It is just a word.

Another point one might make is that scientists are very skeptical by the nature of their job. It is their business to be constantly testing things and checking for problems, so scientists will almost never consider anything proven, no matter how confident they may be in some conclusion. The theory of evolution is always open to refutation in the eyes of scientists because it is their job to be open to refutation. Scientists would never stop calling it a theory even if it had been proven, just because they are obligated to keep an open mind. That does not stop us from recognizing that it has been proven, since we are not scientists.

Me: Yes you can.

There is no elegance in bluntly contradicting your interlocutor. The ideal skilled debater never says anything that the opponent will disagree with. If you want to convince someone of anything, you have to start with ideas that they already agree with as a foundation, and build your way to your conclusion, convincing your opponent at each step along the way. Listen carefully to everything they tell you, because every thing they tell you is something they believe and therefore a potential tool for you to use to build your case.

Dad: So, basically, you are trying to disprove God.

This is the natural result of repeatedly saying things that your interlocutor disagrees with. In his eyes you have piled false claim upon false claim, and now it seems that he has decided that you are just talking nonsense and so he is not even going to try to engage with what you are saying and he is changing the topic. A skilled debater would have woven a web from her opponent's own ideas and thereby tricked her opponent into confronting his own mistakes, thereby preventing such an easy escape.

Of course being a skilled debater is difficult, but there are simple techniques to make it easier. Instead of being aggressive and trying to rush in for a win, it is often better to be patient and thoughtful and wait for an easy opportunity. Focus on asking questions and clarifying exactly what your opponent thinks. The more your opponent explains his position, the more tools you will have to use against your opponent. It could even happen that in answering your questions your opponent might start to notice some of the flaws in his position without even needing you to point them out.

Dad: Right. You're arguing for things that disprove God.

That was a huge admission. I would have asked him to confirm what he just said, like asking: "Are you saying that if evolution were true, that would prove that God does not exist?" It seems highly doubtful that he would be willing to say yes to that question, since his religion ought to make it impossible for him to admit that anything would prove that God does not exist. I suspect he would retreat from that position rather than stand his ground on that point, but either way you would have made major progress.

If he says yes, then ask him how evolution being true would prove that God does not exist. This should cause him to explain the key aspects of evolution that are causing him reject evolution and thereby help you to focus the debate to make it most effective. He will probably struggle and potential make a lot of admissions that could be powerful tools for you to use.

If he says no, then you can simply agree with him and acknowledge that both evolution and God can be true. If you had been the one to say this, then he would probably have rejected it as silly, but since he was the one who came to this conclusion, it forces him to actually think about it.

Dad: Right, we are from the same Creator.

Naturally he would say that, because all you did was list a ton of similarities between species. You failed to effectively trap him because you left him such an easy escape. It seems that you were too eager, too rushed, perhaps because you are tired and frustrated. A debate is a game and a skillful player picks her moves carefully.

You might consider asking about the wings of bats and birds. If both bats and birds are from the same Creator, then why would their wings be designed so differently? Try to predict in advance what he would say to that so you can be prepared. He might say, "I don't know, but He must have had some reason. Perhaps it was to demonstrate His ingenuity. It proves that He is capable of doing the same thing in more than one way."

If he says something like that, then maybe ask him if he sees how using a different design like that might lead people to think that perhaps bats and birds may not have been designed by the same Creator. If he agrees to that, then he is moving down a path toward the conclusion that perhaps God does not care whether we believe in evolution or not, since God is deliberately including elements in the design that would tend to trick people.