@BillBarth already pointed out that you are going to get a lot of opinions on this, here is another one:
First of all, I agree with Bill, if it was just about attending the conference (and ignoring the funding) and there is only one slot, then the first author should be the one presenting the work.
However, it is not clear by whom the funding is. If the funding is given by the conference then the funding should, in my opinion, go to the first author.
But most of the time the travel expenses are not paid by the conference but the university (or a grant that was acquired by someone) to give the researchers of this university/department to opportunity to present their work.
The clearest case would be, if the funding comes from a grant given to the lecturer. Here it is pretty clear that he can choose who should be going to this conference. But also in the other cases (grants given to the department/university) the same idea still applies (but maybe to a lesser extend): The funding was acquired to support members of the department: The member of the department should be given priority over the student.
In general, I would advise you to think about it from a different perspective: If this would have been a solo authored paper (by you), would you still have gotten the funding? If the answer is a very clear 'yes', then I would advise you to talk to your advisor again (keeping in mind, that maybe a good relationship with the person who writes your letters of recommendation might be worth more than attending a conference). If not, just let it be and be glad that your work is going to be presented.
A minor remark: In some countries it might not be possible to give travel money to students who are not employed by the university. This is here clearly not the case, but should be mentioned nonetheless.