It's not that they can't meet. Meetings can and do happen and there's no medical reason they can't. In fact, most organ procurement programs have a system in place for allowing donors and recipients to meet.
An example policy:
Does a donor family learn who receives the organs?
The identity of both the donor and the recipient are kept anonymous.
If the donor family and/or the recipient wish to do so, they can
exchange letters through UW Organ and Tissue Donation. After an
exchange of letters, a signed release of information is required by
both parties prior to UWHC releasing any information to the parties.
At that point, if both parties would like, a meeting can be arranged
at a future date. Either or both parties have the right to remain
anonymous and the privacy of both parties is protected by Federal law.
It's long been standard practice to withhold donors' and recipients' identities from each other for privacy reasons. As the above notes, telling either of them the other's identity would violate medical privacy laws in most countries since that information tells them something (perhaps a lot) about that other party's medical history. If identities are made known, it would definitely require written permission from both parties.
But even without privacy laws, there's little or nothing to be gained by either party knowing the other's identity, and potentially a lot of conflict. For example, a family that has lost a loved one might very well not wish to be reminded of that by a recipient contacting them. And vice versa -- recipients might not want the discomfort of meeting the parents of the dead 16-year old whose organs are now theirs. It could be embarrassing, uncomfortable, and emotionally disturbing. There's also the risk of mental/emotional instability from either party. Can you imagine the nightmare of grieving parents feeling they just had to have a close personal relationship with you because you're walking around with their daughter's liver?
Granted, marrow donors aren't usually deaths, but all the same principles still apply. In short, this is an ethics question, not a health question. There is no medical reason marrow donors and recipients can't or shouldn't meet.