There are many types of boys who fit into this “push out” category. Some are just not metzuyanim. Some are academically good or better, but struggle with any of several social issues. Sometimes the boy is a victim of bullying, in which it is typical that the bully is retained and the victim let go. I personally know boys in each of these situations. Sometimes the boy lacks the internal motivation to learn, and while compliant, lacks the “bren” that is expected. There are those who do not “tow the line” with regards to the chassidus and Rebbe of a particular chassidishe yeshiva. There is a parallel to this in more Litvishe yeshivos, as well.
The bottom line is that the Chazon Ish (who was niftar in the early 1950’s) stated that the initial mission of yeshivos after the holocaust was to transplant mosdos for Torah learning, which was to insure the tzibbur had this pillar of existence. But this had already been accomplished, and the mission needed now to focus on the yochid, the individual, to insure that each talmid was guided to their potential success. That dictate of the Chazon Ish appears to have been utterly ignored by most of what we identify as mainstream chinuch. When we have a talmid that needs the extra individual attention, the situation is perceived as “another headache”, or a drain on the yeshiva and its rebbeiim. These are the talmidim that get pushed out, to preserve the image of the yeshiva.
Much of the time, the kids that are pushed out are labeled as cancers that spread and destroy other boys. That justification is used continually, and is rarely true. But once a menahel says it, the boy is labeled, and this even justifies those menahalim that follow the pushed out boy with negative reports, preventing another yeshiva from accepting him.
I know I have just listed a stack of accusations. Trouble is, they are true and accurate. Instead of throwing dirt at chinuch, it is more effective to seek contacts with those in positions of authority, and gradually bring about change in how yeshivos address their mission in chinuch.