How can my wife be charged with a crime if I did not press charges?

I assume you are talking about an assault family violence case? She can be charged and arrested because the police were called to the scene. They make a report and present the case to the prosecutors' office who decides if charges will be pressed. You are a witness but not in control of what happens in the situation / case.

It is the State of Texas that technically files the charges. They may have problems proving the case, but cases are filed every day with individuals not pressing charges.