People (some times kids themselves) ask me this question frequently. Why does a 15 year old that came to the US as a kid can have a work permit and I a 14 (or younger) year old do not qualify for it?
The answer to this question is actually quite simple: deterrence. The US government entities in charge of immigration matters, want to make sure they deter people (mainly parents) from coming to the US illegally with their minor children and then, once they cross the border, apply for available deferred actions or programs that provide work permits; or that pseudo legal status deferred actions provide.
Lets put a simple example. In 2009 Juana wants to come to the US illegally with her 5-year-old boy Miguel. She manages to do so. In 2014, President Obamas signs an executive order (DACA), which allows children who came illegally on or before January 1, 2010 (and meet some other requirements including 15 years of age when applying) to obtain a work permit. As it turns out, Miguel will not qualify for this benefit because he will only be 10 years of age. Miguel will have to wait an additional 5 years to be able to apply for DACA.
The message the government gives you with these requirements (whether it is a particular age, or length of physical presence in the US) is that; if you plan to come here illegally you (and the kids you bring) are going to have to wait a very long time to have any kind of legal status. By the time Miguel is eligible for DACA he would have waited around 10 years.
There is, however, an exception to the 15-year rule. If Miguel is in removal proceedings, or has an order of deportation, then Miguel would be able to apply for DACA. Thus, assuming Miguel is otherwise eligible, Miguel should not be too worried about being kicked out of the country because, in fact (and ironically) a removal process started against Miguel would make him eligible for what he actually wanted: DACA.