Why do republicans not support gun control?

Generally speaking, because they believe gun control does nothing to keep guns out of the hands of criminals. The assumption is that criminals obtain guns illegally, and no amount of new laws will change this already criminal behavior.

Also, it can be seen as a conscious decision to favor certain rights over others; this is inevitable, as when two rights conflict, one must choose which has precedence. In this case, Republicans choose to prefer the guaranties of the 2nd Amendment over those from other sections of the Constitution.

Finally, there is a practical political dimension to this. The National Rifle Association is a firm supporter of very minimal gun regulation, and is a large and well-funded organization. In fact, it has been called the most effective and powerful lobby in politics. Adhering to the NRA's position is means political support (in terms of votes, money, and advertising) from the NRA.