Your subsidy argument is based on the fallacy that the government is owed that tax money to begin with.
It isn't.
The reality is the government is going to take in enough money to keep itself running regardless of philisophical debate on whether that money is "owed" or not.
Cuts to individual taxes don't occur in a vacuum. The money the government is going to spend has to come from somewhere - for every dollar less of it that comes from Peter, a dollar more will come from Paul.
Needless to say this is quite popular with Peter.