Their difference
Because he is an alien and she is a human.

The protection
Max tells Liz that they cannot be involved because she will be in danger. He tries to protect her acting like this, but they only hurt each other's feelings.

The Control
Because Max believes that he lost control when he is with Liz, he takes a 'step back' in their relationship leaving them as friends again, at the end of 'Balance'.

Tess & destiny
She is the fourth alien and is supposed to be Max's infatuated mate. He is attracted to her even if he loves Liz. Unfortunately, the message of their mother confirms that he should be with Tess.

Consequences of destiny
Liz refused to let herself be with Max again in the first episodes of season 2, scared of the consequences and thinking of the benefits for others.

End of the World
Max from the future came to see Liz and told her that in the future they were married and Tess left Roswell. Therefore, the aliens were not as strong and the Skins invaded Earth killing Isabel and Michael in the future.