This is a good argument I think. It rests on the logical rule of modus ponens -the way of affirmation. IF a–>b, a, therefore b. So in this case the argument is modus ponens just longer. There are equally valid though wordier ways to express this same statement like for instance, If a–>b, therefore a–>a&b (the principle of absorption) but it is basically the same. In general, I think the biggest ways people kill arguments is through circular argument (assuming what you need to prove), glittering generality (I’m in favor of the poor so I’m going to have welfare -who isn’t in favor of the poor? Just because you are doesn’t mean that welfare is necessary), or the charge of hypocrisy which is lame because even if you were a hypocrite it doesn’t necessarily mean you’re wrong.