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I think it's easier to imagine the reverse problem: if all 44 sparrows are in one tree, can they move to occupy all 44 trees? Suppose the trees are numbered 1 -44, and they all start in tree #1. In pairs, then, they could move outwards until trees 2 - 22 on one side and 24 - 44 on the other were occupied, leaving two birds in the first tree.
The other 42 birds now play no further part, since they are in their correct positions, and the problem reduces to just the two remaining birds. They can now only move in such a way as to maintain symmetrical positions either side (or on) the line joining tree #1 to tree #23. Hence it is impossible for one to remain on (or return to) tree #1 while the other moves to occupy tree #23.
Clearly, we can reverse this, and, starting with one bird in each tree move the birds in pairs to occupy tree #1 until all the birds are there except the one in tree #23. It is then clearly impossible to navigate this bird into tree #1 without disturbing at least one of the 43 birds already there.