What is it called when you say something but it does not imply for the other?

I'm really lost for words...

For example, I like people with short hair. But then someone could say, so you hate people with long hair? But, of course, I did not give any information on people with long hair. I could've liked/hate it. What is this called? I'm sure there was a name to this, maybe an expression?

This is commonly known as the fallacy of "denying the antecedent".

To see why this is the case, you can rephrase your statement as follows.

Let P be "A person has short hair", and let Q be "I like them."

Then by simple substitution, your friend's false assertion is logically equivalent to

P implies Q.

Not P.

Therefore, not Q.

This is the exact formal definition of denying the antecedent.

Here's the statement substitution:

"A person has short hair" implies "I like them".

"This person does not have short hair."

Therefore, "I do not like them".

If someone made that assertion they would be constructing a false dichotomy.