There are many forms of the Ontological Argument for the existence of God. The following is Wikipedia’s optimal modern description.
1. God is that entity than which nothing can be greater.
2. The concept of God exists in human understanding.
3. God exists in one’s mind but not in reality.
4. The concept of God’s existence is understood in one’s mind.
5. If God existed in reality, it would be a greater thing than God’s existence in the mind.
6. The final step to God’s existence is that God in reality must exist.
The Ontological Argument strikes me as the equivalent of trying to win a lawsuit on a technicality. It’s a full-blown a priori attempted proof which assumes only that a perfect being is conceivable. I won’t argue this point, because although definitions may differ everyone gets some image in mind upon hearing the phrase “perfect being”.
The thrust of the argument is that it’s greater and more perfect to exist than not to exist. Since God in theory is the greatest and most perfect thing ever, He must exist.
The most obvious problem is that the argument is not the least bit specific about which God exists. Even if the argument were unassailable and the existence of a god were proven, we would still know absolutely nothing about the god’s identity or nature. Jumping immediately from the existence of a god to the existence of your god is an unsupported assertion.
If you really wanted to be annoying, you could argue that since the argument can be used to prove the existence of multiple mutually exclusive gods (say, the God of Abraham and Ahura Mazda of the Zoroastrian faith) it’s obviously a flawed argument. The theist reply is of course the above point that the argument makes no comment on the god’s identity and most religions just have the wrong guy, but it’s a good way to make people think.
The real problem is the premise that to exist in reality is greater and/or more perfect than to exist only in the mind. Something which doesn’t exist isn’t more perfect than something which does, but it isn’t less perfect either. It has no qualities by which this can be judged. An apple which doesn’t exist isn’t red, but neither is it purple. Therefore it can’t be redder or less red than a real red apple.
Existence isn’t a property as such either. Even if it were, it wouldn’t necessarily be a positive property, or something a perfect being must have. Something destructive like an earthquake might be better if it didn’t exist.
There are plenty of objections along these lines by a great many people, the most famous being Bertrand Russell and Immanuel Kant. As stated in the question, there are also a great many rephrasings of the argument which try to circumvent these objections.
The net result is that major apologetic organisations have advised that the Ontological Argument in its current forms does not stand up to scrutiny, and other arguments like the Transcendental and Cosmological Arguments (the favourites) should be used instead.
That doesn’t stop a lot of YouTubers from reciting obscure forms of the Ontological Argument and expecting them to be invincible. Look it up, and enjoy the logical knots both sides get themselves into when discussing it.
I always worry when someone uses this argument, because it may mean a few things. Maybe they don’t think people have the intelligence to fully comprehend such a complex-sounding argument and will accept it by default. Maybe they haven’t read the objections and don’t expect anyone to look them up. From a big-picture perspective, they’re using a less well known argument thinking it will take people by surprise, not considering that it’s less well known for a reason. It just plain doesn’t work.