My mother (age 96) shares 102.1 cM with a man (age 72). However, I do not share any cMs with him.
What could their relationship be and why don't I share any cMs with him?
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You don't share any cM with the man because you have a 50-50 chance of inheriting any given segment from either of your parents. While it's uncommon for a 100+ cM segment total to turn into 0 cM in one generation (because segments split up randomly so most children would get a piece of one or more), it can and does happen. Just the luck of the draw.
Going to the Shared cM Project, we want to look for a relationship that accommodates both your match with the man and your mother's match with him.
There are plenty of possibilities. I will only name a few. If your mom's largest segment with him is over 20 cM, it points to a closer relationship than if the largest is under 10 cM, say.
There is a 50% chance of you inheriting each segment your mother matches on. With your mother matching 6 segments, there is therefore a 1/64 chance that you don't match on any of the segments your mother matches on. That's a pretty low probability, but is possible.
That's assuming all your mother's matches are real. Any match below 15 cM might be a random match.
Try to investigate the people your mother shares in common with this man, and see if you also share with the in common with people. That might help you narrow down how this man is related to your mom and to you.