I normally do not object to people linking to their own web sites as part of their signature. In the case of this particular posting/thread, it reads like an advertisement, it functions as an advertisement, and by allowing the web site to be mentioned anywhere in the posting (including the signature) I would be condoning that advertising, which I will not do.
In my opinion, you would be free to include links to any web site for additional explanation of any point you were making as a response to a question. You would be free to include a link to your web site in your sig as long as the associated post is not an advertisement for that web site or your services. That particular post reads like an advertisement to me, so I can't condone allowing any link on it, even in the signature.
This is a gray area, and one that requires subjective judgement because it is so close to being outright unacceptable. I have no quarrel with you, and other moderators have strongly encouraged me to give you the benefit of the doubt (which I think that I have done, I normally ban users that I perceive as spammers without discussion).
Yes, you can appeal my decision. You can PM me a phone number so that we can discuss how you can make that appeal.
-PatP