A lot of those apologetics assume that God does have limitations. Bonus points of the apologist still claims he doesn't have limitations. Common examples include:
*This reminds me of a thread I want to start.
- Free will - we need to be able to be free to sin because [reasons] and this is super important. Now, why an all powerful God couldn't make us have choice, but only good choices is beyond me.*
- You have to know dark to know light - God can't create beings that appreciate good without having suffered first.
- Best of all possible worlds - it implies a limitation by it's very premise. God is facing unstated limitations and he is doing the best he can. The world would literally be worse off if little children didn't die of Tay Sachs. Because [reasons], of course.
*This reminds me of a thread I want to start.