I haven't read the other responses. I strongly believe that men and women can be friends. I worked primarily with men and we formed friendships. However, the man had to be careful to include his wife in the friendship.
You know you're just friends. The wife doesn't know that. What you have to deal with is her perception. Just repeating the friendship part is not working with her. I suggest that you have to socialize with her so that she can see that you're just friends.
Yes, this change in your relationship is painful. I get that. Now you have to decide if you're willing to accept that change so that you can become friends with his wife or if not, let go of the relationship. Above all work at seeing this from his and his wife's viewpoint. Be sympathetic and not judgmental while you think about the ideas that have been written.
I would schedule an activity that included all of you including your significant other. If you aren't a part of a couple, I can understand her distrust even more. I was single and some wives didn't want their husbands being alone with me. Fortunately, the deputies did things together so that I was rarely alone with one man. If I was to socialize with a married man we included the wife.
Another thing that is hampering your friendship is that you don't like the wife. Even if you think you're covering your feelings up she can sense your disapproval. Would you like for your husband to have a friend, either male or female, who didn't approve of you?
I urge you to find a way to like the wife. Do you have anything in common? Can you sympathize with her insecurity? Can you stop judging her as being inadequate for her husband? She senses your feelings. I understand her jealousy.
I suggest that your friend needs to figure out how to provide his wife with more security. I understand his not getting together with you. Good that he tells his wife when he runs into you. Encourage him to do that. Also, respect that it's not good for him when you're seen as a threat to his wife. Respect her wishes and respect his decision to stay away. Don't put pressure on him.
Whether or not you get together is his decision. I'd respect him for respecting his wife's wishes. He is married and that has to change your relationship with him. He no longer has the time to talk 2-3 times a day. He doesn't need you when you put a strain on his marriage.
I suggest that if you can let go of your jealousy and begin to accept his wife that you could become a part of THEIR circle.
I've now read the other responses. Only 1 person said that men and women cannot be just friends. As to asking questions here, if you don't want to hear another side to your situation, don't ask the question.
I urge you to really think about what is said here. If you don't understand or agree with the answers then ignore them. When you become angry and defensive you're saying that we've touched a nerve with you and you know on some level that some of what is said is true. If it weren't true you could say, well that's their opinion. I don't agree, without getting emotionally upset.
Please take a good look at your expectations. You cannot be his best friend any more. To have a friendship at all you have to respect him and his marriage.