Dafür vs. dagegen können

Question

I get how dafür and dagegen are used in the sense of being for or against something –from today's news:

"Ich bin dafür, die Sanktionen schrittweise abzubauen, sobald es zu Fortschritten bei der Umsetzung des Minsker Abkommens kommt" (Sigmar Gabriel)

Similarly, I can use dagegen to express that I have (or don't) something against something or someone:

Ich hätte nichts dagegen, wenn wir zwei Wochen Urlaub in Italien machen

Things get a little confusing, though, when we talk about doing something against something, or the ability to do something about something (especially something negative). For example, from Der Postillon:

Mann, der zufällig aussieht wie Adolf Hitler, fühlt sich diskriminiert.

Er kann kann doch nichts für sein Aussehen.

I would not intuitively use für here. On the contrary, I would use gegen, since it's something I presumably don't want but can't do anything about. I'm going on the assumption that this is also an example of the supression of the verb in the presence of a modal (i.e. können actually stands for tuen können here) ⁽¹⁾. I'm often unsure whether I should say Ich kann nichts dafür or dagegen when trying to express that something is out of my control. So this makes it even more confusing:

Internet langsam: Was kann ich dagegen tun? (Giga.de)

Again, this is something negative that I'd like to do something against. In this case, though, it seems that there is indeed something I could do about it. So does it lie precisely in the fact that in the latter, the subject can actually do something about it, whereas in the former he can't? Is there a difference between "ich kann nichts dafür" and "ich kann nichts dagegen"?

Thanks.

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(1) Actually, this is incorrect as was confirmed in this subsequent question

Answer 1

"etwas dafür können" or "nichts dafür können" (there is no "etwas dagegen können") means wether something is your fault or not or if you are responsible for something that happened or not. It does not necessarily express if you are for or against it or if you want to do something about it or not.

You could say:

Ja, ich bin reich geboren. Aber dafür kann ich ja nichts.

Ich bin jünger als du. Dafür kann ich nichts.

So the example about Hitler is not really comparable to the other examples. You could change it to:

Er kann doch nichts gegen sein Aussehen tun.

And then it is comparable to your last example, but it changes its meaning. Because now it's not about wether it is his fault or not, but about if he's able to do something about it or not.

You could change the last example about the slow internet to fit the example about Hitler, then it would be:

Langsames Internet. Was kann ich dafür?

Now this would mean: "Slow Internet. Is it my fault?" (so you think you did something wrong which causes the Internet to be slow)