I hate to say it, but I think you've hit upon what drives a lot of the "anti-tithing" mentality.
People justify not tithing so that they can spend it on themselves. "It's MY money, I'll do what I like with it. Maybe I'll give some or maybe I won't."
Completely unscriptural and ungodly attitude. God says that it is ALL His - we merely have what we have on stewardship.
Straw Man.
You left out a third option: it isn’t part of the New Covenant program, as the New Covenant is silent on this, and Christians are to go by the New Covenant.
So why should one be obligated to follow the Old Covenant, when as Paul says, it is “old, obsolete and ready to vanish away” - a covenant of ordinances that were “nailed to the cross.”