A biallelic GM is when BOTH copies of the gene receive the genetic modification instead of just one copy. With most methods all or the overwhelming majority of organisms receiving a GM get only one copy and then you have to reproduce it (unless you lucked out and go a breeding pair) to get a breeding pair and then cross them to get homozygotes (organisms with two copies of the GM so that they will "breed true".)
Immune cells, of course, don't have sex but reproduce clonally. So you can't take two cells with mono allelic (one copy) GMs and cross them to get biallelic cells.
Sorting monoallelic cells from biallelic cells is also a major headache. So the best way to get large numbers of cells with a very high percentage of biallelic GMs is to develop a method that gives a high rate of biallelic GMs on its own.
For the CCR5 deletion for treatment for HIV, a cell that is only mono allelic for the deletion is still only partially resistant to HIV infection, it takes a biallelic GM to make it totally resistant>
(a monoallelic deletion still has one normal copy that produces funtional CCR5 and it will be present in the cell membrane, just not as much of it (as a cell with two copies) so the infection rate will be lower but NOT zero. )
NOTE that for the patient who was natuarally heterozygotic for the CCR5 deletion (there was ONE) ALL GM's were biallelic because there was already one copy of the deletion. So HIS levels of injected biallelic modified cells was much higher and that was what was responsible for this far better results.
Now they want to be able to do the same for ALL patients.
(my apologies for previous reply that accidentally posted without any content! Not sure why)