The act of self-titling has a long, glorious past. False princes and pretenders come to mind.
One who takes on the responsibility of self-titling may be well-intentioned or not; they may puff themselves up or put themselves down. However, it is far more likely that they will go in the self-important direction; those with low self-esteem tend to use the reverse of a title, i.e. "oh, I'm just some girl". (Note the use of "some"--these people are not even calling themselves a specific being.) Overconfidence, on the other hand, often plays a part in the act of actually titling oneself something positive, and hence in the case of calling oneself a poet.
A poet, like a doctor, a lawyer, a king, a dead ringer, a pharmacist, a magistrate, a priest, a mother, a father, a programmer, a peer, or a friend, is a title indicating a personal status. Many people think that they deserve this title simply because they have written something which they think of as a poem, or a body of work which they categorize as poetry.
So the question becomes, who has the right to say that a given work is poetry?
I feel that writers (and artists as a whole) in general are too close to their own work to view it objectively. Anyone can write something they are impressed with; anyone can write something they hate. Other people are probably going to have a large range of different responses to any given work, however. In this case, it is others who get to decide whether a given person can be called a poet.
Let's not even dispute who these "others" are right now. The important thing is that they are not the person whose title is in question.
Therefore, calling oneself a poet is presumptuous.
It can also be a bit pretentious. Many people who call themselves poets feel that they must act like a poet in order to prove their status. And they define "acting like a poet" themselves as well. This is unfortunate, and can result in a lot of kids running around with their copy of Ariel and their triple mocha lattes, wearing long scarves and sneering and scribbling desperately in the corner of a cafe. This is not altogether a bad thing, especially if it helps them deal with whatever stress they are going through, and I would be surprised if writing did not. But it does not make them poets.
Calling oneself something does not make it true; being generally called something, i.e. being known to be something (in fact, being that something) does. This is the case in language theory. If you decided that from now on, all ducks would be called giraffes, and published a declaration as to such in a newspaper, this would not make people either call ducks giraffes or think ducks were giraffes. The title of this particular set of creatures would not change just because you say so; you do not have the authority to change this, and you certainly cannot make ducks BE giraffes (unless possibly you study ducks for a living and are a renowned expert in the field, but even then, I am sure some other scholar would dispute your findings, and there would be a large upheaval within the academic community, and after all that people outside the academy would still continue to call ducks ducks instead of giraffes).
In the same way, you cannot make yourself into a poet by giving yourself that title. You cannot change the nature of something simply by declaring that it is something else, except in specific cases. Likewise, if you do not understand what it is a poet does, then you cannot just start acting like a poet. And acting like a poet does not make you one either. You have to be one.
I personally say "sometimes I write stuff." So far, that is the closest thing to what is true.