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Because it means you have to compromise. And if the other shareholder is difficult, everything becomes time consuming and difficult. Unless you have a great relationship with the other share owner, it's a ball ache compared to being a leaseholder, providing the other flat is leasehold too and you have long leases. In that situation you can at least gang up on the freeholder if they try to stiff you.
If you are the sole freeholder, and resident, in a two flat property, you can do what you like, pretty much, within the grounds of the law and the existing leases. IIRC the leaseholder cannot force you to sell a share to them, and you can impose service charges and all sorts of nonsense, threaten major works to get them to do what you want etc. It really is a nightmare for the disenfranchised leaseholder.
Honestly speaking I wouldn't even want a share. I'd want the freehold. In a flat that's divided in to two flats. There's no benefit in having a share. There's a huge benefit in being the freeholder.
I suspect he knows this, which is why he wants to put @dbr off from getting involved.