Hey Aki, I can see how you've been confused.
Counting on someone is the ability to rely on them, trusting them to do or be something. For example, when you need your sister to pickup something for you, you are counting on her to do it. Or if she is not reliable, you are not counting on her to do it.
However looking to someone means to turn to them, for something that you would like from them. For example you can turn to someone for support, for love or even for laugh, etc.