Your question suggests two lines of thinking. ‘Stupid and unoriginal’ as a general feature of the arguing person is too broad to be brought down to a single term, but your further description suggests ideas like blinkered, short-sighted, bigoted or jingoistic. These all relate to an unwillingness to acknowledge ideas beyond an already-assumed frame of reference.
On the other hand, you also describe an outward-looking strategy of attacking a perceived opponent’s credibility. In formal logic this is known as the ad hominem fallacy (literally ‘at the man’, as John Clifford has noted near here): the sleight-of-hand of avoiding inconvenient points by decrying ‘the man’ (male or female, obviously) rather than addressing what that person has actually said.
Politicians do this routinely, and you have probably been personally infuriated by it here and there in daily life. In pub banter it is simply a laugh to say, ‘That’s exactly the kind of rubbish a gay midget like you would come out with,’ because we all tacitly acknowledge its logical irrelevance. Over a serious matter, however, that kind of approach is generally seen as intellectually evasive and cowardly. Whatever I think of potential-President Donald Trump, for example, I have no time for anyone dismissing his politics on ground of wig-ignorance.
Referring to someone as a ‘tree-hugger’, similarly, is the mark of someone not addressing the issue, but still trying to ‘win’ a discussion (about anything at all) by creating the image of an unrealistically romantic hippie.
Of the terms you suggest, ‘weak argument’ and ‘lame excuse’ certainly apply but are very vague. What you describe is certainly ‘changing of the subject’ in the sense of suddenly arguing about someone’s age or menstrual state rather than the subject at hand, and if that is the specific strategy you have in mind then ad hominem argument is what it is technically called.
Other terms that might be relevant include browbeating, bullying and generally avoiding the issue. Some proportion of hypocrisy could well be in the mix. Any or all of those might be appropriate, depending on relative emphases within the argumentative style you are describing, and what it is trying to achieve.
You could also consider defensive or reactionary, to describe either the person or the rhetorical strategy. Your portrayal of this character sounds misogynistic and overbearing, but to be fair he might just see himself as beleaguered and repelling boarders, like the strangely sympathetic sitcom bigot Alf Garnett.
