When is it not good to be assertive?

When it is not your role to decide, typically. Assertion claims a right to say, to determine, to tell others; assumes a role of authority. If you do not have that right by role or position, then you should not be trying to tell others what to do or say, or what is true or false, or right or wrong. Who died and made you king? type of idea.

The only authority you possess by your very existence is authority over your self. All other authority is either earned, or granted by others (whether or not it is deserved). Sometimes you have to assert yourself to force others to recognize your right to authority. Other times, that is precisely the wrong thing to do because you do not have that authority you are trying to assert.

When assertiveness becomes aggressiveness

When you're not sure if the other guy is a homicidal maniac.

When you seem pushy or when you're too overconfident on something and you're actually wrong

About your own personal things likes or dislikes, lines you won't cross et al you can be assertive, but never force your will on the other person

When you really really DO NOT want something.