Many Texans conceptualize government and state uses of force (ie prosecution that can lead to imprisonment) as restrictions on their rights. This "negative rights" conceptualization is pretty common in the US, but especially common in Texas.
In the specific case of using deadly force to prevent somebody from stealing your property at night, the idea is something like the following. Absent any government intervention, you have a "property right" which allows you to prevent the thief from taking the property. In some cases, the balance of public policy concerns should lean in favor of government restrictions on this property right, to protect potentially innocent people or to prevent nonviolent criminals from dying, or to sustain an orderly justice system without vigilantes.
However, many Texans believe that the government should not intervene in this case because the restriction on an individual's right to protect his/her property is more important than the other policy goals.
Like I said, this is just my attempt to articulate the way I'd guess many Texans feel about this. I don't necessarily agree with all of the above.