I think the answer is because they simply support attacking and targeting human rights organizations, such as gay rights organizations, or ones that protect targeted minorities.

I tried to get them to talk about this issue, and they basically admitted that they support removing, for example, gay right organizations from the internet, via DDoS attacks.

Because apparently protecting gay rights organizations would infringe on their free speech to target and remove those organizations from the internet.

Well, yes, it would indeed infringe upon such a right (if it existed), but this argument can be applied to any action. The fact that murder is illegal infringes upon my natural right to shoot kelseyfrog in the face. If they want to argue for total lawlessness I won't stop them, but it would be less disingenuous if they would stop beating around the bush.

The content of the idea is superfluous. The point is that if you give the government the ability to tell people what packets they can and cannot send, then you're implicitly trusting that they won't abuse this power in the future and decide that there are other things people can and cannot send.

You're avoiding the question. Your claim is that making DDoS attacks illegal infringes upon your right to freedom of speech. My question to you is, since freedom of speech is the freedom to express ideas, what idea does performing a DDoS attack express?