I'm sending you pictures of my activity, my husband's, his time in the segment, and the segment itself, which completely matches my activity but is not visible in it.

https://www.strava.com/activities/15288620029/segments/17536763/potential-segment-matches

The potential segment matches for your activity are only visible to you. Anyway I would guess that the GPS differences between your activity and the segment added so much up that the segment couldn’t be matched anymore.

I’ve looked at the segment too and to be honest, whoever created it hasn't done a great job:

The ending looks pretty weird, it should have been cut off earlier. I suppose that can cause matching issues.

But also - your turning point seems to be a bit earlier than where the segment goes:

Yes, the end of the segment is too bad but I did this segment over 150 times and I know good where is it. Also my husband did the same activity and there is segment До Синия вир...

​@vanya.y.yordanova - Just getting to the end of the segment doesn’t mean it is going to register on your recording.  You really need to go beyond the end to ensure there is a data point past or close enough to the official segment endpoint, otherwise it won’t match.  It is just luck of the draw that you husband's device recorded a point close enough to the end to register that he completed the segment.  If I am ever really shooting for a good time on a segment, I will make sure to continue the effort at least 20 yards beyond the end, often further, to help ensure that I get a good data point beyond the end of the segment.  

I know that. But the segments: До Синия вир последна част, Синия вир спускане 1 част , Синия вир спускане and До Синия вир и обратно are part of the missing segment! There is no logic that only one segment До Синия вир is missing . I did it so many times, only this day this segment was missing...

Looking at those other segments, here is what I see.  До Синия вир и обратно turns around right where you did, so was included.  Синия вир Спускане stops before where your file shows you turning around, so it was included.  Синия Вир последна част stops earlier than where you turned around, so it was included.  The segment you are not matching, До Синия вир. shows it going beyond where your file shows you turning around.  End points of segments are critical matching points for the Strava algorithms and your file does not show you going all the way to where the endpoint is of the segment.  I would not expect that segment to match.

Here are side by side photos of your activity file showing where you turned around and where the segment you want to match ends.  You can clearly see that your file does not show you going all the way to where the end of the segment is.  Start and end points are critical matching points when trying to match a segment to an activity.  If it doesn’t show your activity clearly going all the way to the end, if not beyond, it is not likely to match.  Keep in mind that GPS devices aren’t 100% accurate, so two people running together likely won’t show exactly the same track.  Your husbands file could have some “drift” that put his turnaround point close enough or beyond the segment end point to make a complete match.  

Thanks for the comprehensive answer! Stay safe, I'll do it again!