TLDR: Focus on graduating as soon as possible, only use your advisor for things directly related to that goal. Do not use them for emotional support.
The current top answers focus on seeking counseling* and exploring other professors** in the department. Those are reasonable options, but I think miss the mark a bit.
Your advisor has stated he "doesn't think the subject is for you," and that you haven't made enough progress, but has offered no evidence to support that. You provide evidence that your progress is sufficient (possibly even more than sufficient), and other than normal temporary setbacks you don't identify any major obstacles to completing your thesis.
First, other than severe lack of progress, it's not your advisor's decision whether to continue your program. As long as you're progressing, that decision is yours alone, and you should only leave the program if that is what you want. It doesn't sound from your comments like that is what you want, so I'll assume for this answer that your goal is to complete your degree.
As others have pointed out, your progression sounds on-track for this point in your degree. Advancing to candidacy and having an approved research plan are major accomplishments that you should be proud of, and are direct evidence of your progress. You describe in other comments that you've authored 3 papers, with one in Nature. If any of these are first-author papers they are also major accomplishments.***
Unfortunately, your advisor's discouraging words, and the difficulty communicating with him, signal to me that he is not, and is not going to be, your enthusiastic supporter. This is understandably very discouraging and an emotional blow.
It is understandable to hold professors in high regard as a graduate student. Keep in mind, though, that being a professor is only evidence that they are a subject matter expert. Simply knowing someone is a professor does not tell you if they are a good manager, communicator, or advisor. It also doesn't mean they're any good at knowing who "has it in them" to accomplish a goal.
You have evidence that your advisor's assertions about your progress are not true. In fact, you don't need your advisor to affirm that you are making progress, you can check that for yourself. You have a research plan that was (presumably) approved by your advisor and committee. This is your progress guide. If you are advancing on your research plan, you are advancing.
With this in mind, my recommendation is to acknowledge that your advisor is not going to have the expanded role most people wish for in the advisor/student relationship. They aren't going to be your cheerleader. They aren't going to give you encouragement. They probably won't give you good career advice.
This is discouraging, but it's not the end of the world (or of your degree). You have a year or two left on progressing your research plan and writing your dissertation. Use your advisor only for the things that are needed to accomplish that. They can (and probably should) advise on experimental setup and analyses. They should be responsive to editing manuscripts and chapters. They should do the paperwork that needs to be done to keep the lab and your position going.
Another answer suggests trying to sit down and making an emotional connection with your advisor. I disagree. I don't think you should spend your energy trying to convince them of anything other than that you are doing dissertation quality work. (This is obviously very personal advice. Only you know your relationship with him, and maybe trying to convince him to be supportive and that you're brilliant is worth it. But at the end of the day all you need is for him to sign off on your thesis, you don't need him to be chummy while doing it.)
You will also need to make sure that he is holding up his responsibilities as an advisor. This means some minimal amount of communication. It means responding to experimental questions and edits in a timely manner. It means acknowledging progress on your research plan. It means providing reasonable lab resources to do your work.
His focus on progress might manifest as a suggestion that the research you've already outlined is not enough for a degree. This is when you pull out your research plan, that everyone signed off on, and ask what has changed to demand more work. Your committee can help with this, too. (My uni had a requirement that committees include a member from a different department to represent the student's interests. If yours has something similar, they can also guard against piling on work.)
Focus on finishing your thesis. Don't take on any extra lab or department duties you don't have to.
Finally, find your allies who will be supportive. Get encouragement and affirmation from your friends, fellow students, and family.
*Counseling is an excellent suggestion, and an appropriate place to work on your emotional needs and get a detached perspective. I see your other comments that you haven't found it very helpful. Consider discussing with your counselor what might help this, and use whatever counseling benefits you have to their maximum.
**Several other answers suggest switching advisors. This might ultimately be needed, but I don't think that's a given, yet. As far along as you are, it might be very difficult to find a new advisor, and you'd spend a lot of time figuring out all the logistical issues in switching, such as funding, space, etc. You might also run into objections from your current advisor (I don't know what their incentives are, maybe a student switching looks worse than one dropping out). You'd have to weigh whether it's worth your time to go through that, compared to putting that effort into your thesis. However, if your advisor begins actively blocking your progress, or essentially abandons you so that you can't progress, by all means, find someone else.
**If all three are first-author papers, you're progress is excellent. If that's the case you should seriously consider how to transform those into the bulk of your thesis. This also may be evidence of actual obstruction from your advisor, because it would be highly inappropriate to suggest that a 4th year student with three papers leave a program.