How did birds come into being?
First we must distinguish between modern birds on the one hand, and their feathered ancestors called "basal paraves" on the other.
Basal paraves were feathered, long-bony-tailed, flying creatures (eg. scansoriopteryx). No modern birds have long-bony-tails.
So the question becomes, how did basal paraves come into being?
The dinosaur to bird theory suggests that basal paraves evolved from coelurosaur dinosaurs (eg. tyrannosaurs).
The pterosaur to bird theory suggests that basal paraves evolved from pterosaurs (eg. rhamphorhynchids).
The topic immediately becomes complicated, because there is a set of feathered, long-bony-tailed creatures that did not fly (eg. oviraptors, alvarezsaurids).
The dinosaur to bird theory views these creatures as transitional between ground-based coelurosaur dinosaurs and flying basal paraves. They call them "non-paraves maniraptors".
The pterosaur to bird theory views these creatures as secondarily flightless* members of basal paraves.
It is important to realize that according to the fossil record, all these flightless, feathered creatures came after (closer to today than) the flying members of basal paraves.
This is straightforwardly consistent with them being secondarily flightless. On the other hand, for them to be transitional between dinosaurs and flying basal paraves, requires purported lengthy ghost lineages (up to tens of millions of years in length) and purported exaptations.
* An ostrich is an example of a "secondarily flightless" modern bird.