Another thing to think about is that occasionally some less experienced pilots have a hard time with 121 training. That is not to say they can't be good pilots, but are just having a hard time keeping up with things if they only have a few hundred hours of experience.
I hear about pilots from time to time at my own company who wash out. We have a solid training dept and they are big on attitude. But attitude will only get you so far and washing out of a training program would be terrible for you own morale and also might make it more difficult to secure another interview later.
Just my $.02.
I am not trying to be negative, but if you get your MEI or a 135 M/E job and some real M/E experience you will probably have a much easier time with 121 training.