Several arguments can be made against making such resolutions. In the first place, they almost always fail. Second, the division of time by years is somewhat arbitrary anyway: the fact that it is 2016 now rather than 2015 is determined by convention, not by any particular objective distinction between the two years. If we wished, we could choose some other day as the start of the year.
One can respond to the first argument in two ways, first by saying that even a low success rate could be a good reason for making such resolutions, and second by saying that there is no need to make such a black and white division between success and failure. If you make a resolution and keep it for five days, that is five days of success, even if you fail to keep it for the remaining 360 days of the year.
In any case, a good reason for such resolutions is that human beings are not consistently guided by reason, but often by emotion and habit. Consequently we have certain goals that we suppose we are seeking according to reason, but our concrete actions frequently fail to be proportioned to those goals. A resolution can be seen as a renewal of someone’s intention to act according to reason. According to the second objection above, there is no objective necessity for this to happen on January 1st rather than on some other day. And in fact, there are good reasons to renew your intentions on a much more regular basis, such as every month, every week, and every day. If we accepted the second objection and decided that there was no reason to renew our intentions on any regular basis at all, it would be quite likely that we would fall into a kind of laziness and never renew them, not even on an irregular basis. So there are good reasons to choose the divisions of time which are determined by convention, even if in principle we could choose other times.