First of all, Remus was a werewolf, and the werewolf was a low-ranking and tortured species in the wizarding world at that time. So Remus didn't have many good friends himself. Secondly, his good friends are well known. There are three of them: Sirius, james potter and peter pettigrew. Only james potter has children. Generally, a respected friend who has a very good relationship with him will be asked to be the godfather (babies or children will be given Christian names when they are baptized and promise to undertake his religious education), which is a foreign tradition. As we all know, when Teddy was born, Sirius and Zhan Mu were already dead. Peter pettigrew is not only a death eater, but also directly killed Zhan Mu and Lily and indirectly killed Sirius. So it's impossible to invite him!

It is obvious that Harry is the best choice at this time, and because Remus is Tonks' husband and Tonks is Sirius' cousin (Sirius is Tonks' cousin, and Sirius once said that Tonks' hemp is his favorite cousin). Sirius is Harry's godfather, so Harry's qualifications are higher than Teddy's, so he can be godfather.

And Harry's experience, his personality, his education and his own quality all make Remus think he can be a qualified godfather. I think it is also a very important reason.

PS: Because the content of the question belongs to a book without details and hints, it belongs to my subjective speculation. If there are any mistakes, please point them out and discuss them. Any provocation and quarrel are not welcome.

Thank you for reading and hope to adopt it.