As a native speaker,
- "Timing" is a valid word, however, it is not used properly used here. I think "miss the right time to enter" is the correct phrase to use here.
The issue is that "timing", and indeed its root "time" are verbal nouns, which means they are used as both nouns and verbs, with differing meanings. "Time", as a noun, means a collection of hours, minutes, and seconds (not an accurate definition, but a useful one). As a verb, it means to measure the passage of time (the noun). Timing as a verb is the present tense of the verb time. As a noun, it means "Synchronization".
As an example, if my timing is off (which is how one generally says that the timing is bad) to catch the bus, I am either early or late, and must wait. If my timing is correct, I arrive when the bus is at the bus stop, and I can board.
As TRomano states, timing can be used to mean opportunity. If one is synchronized with employers, schools or training programs, one will be ready when they are hiring or enrolling, and can be hired and enrolled. If one is not synchronized, then one will not be hired or enrolled.
For example, if a given university has an application window (a period of time in which one can apply) consisting of the first two weeks of March, anyone who applies in May will not be considered (although at some institutions, it may be accepted for the next semester/year/class, etc.), because their submission of their application was not synchronized with the application window.
- "And" correctly joins the two reasons that/explanations for why NEET is problematic. In fact, I would say that "And" is the first choice to join two positive statements.
