Does "associated with" imply a certain hierarchy?

I have two items that bear a certain connection, and I want to describe this connection using the word "associated".

If I want to say that A is associated with B, does this imply that B is greater/more important than A? Or can I just as well say that B is associated with A?

As an example, I could say:

I am associated with Company X.

but it seems wrong to say

Company X is associated with me.

But is it OK to say something like

I am associated with my team mate

(where the two of us are equals)?

Good question.

I think there are three scenarios (not considering the 'spend time with' sense of 'associate with'):

(1) non-commutativity (ie the order A is associated with B is not reversible):

I am associated with Macrosift.

(2) commutativity, both syntactic and semantic:

Wealth is associated with freedom.

(3) commutativity, syntactic but not semantic

Klausenheimer was associated with (involved with ... / instrumental in) the Monhittan project. (Though note that the 'reckoned to be involved in' sense, almost the reverse of the next sense, is an alternative reading here.) ...

The Monhittan project was associated with (regarded as being the brainchild of) Klausenheimer.

All these senses are available. If context does not differentiate, a rephrasing is advisable.