In my opinion you should listen to your trainer..
Its always more comfortable to fight holding your arms down or by your side but in all fairness.. Its not good for you..

For one you are too inexperianced to hold your hands down herre.. You dont have the ring savvy yet to be aware of shots coming and all thats going to happen is you'll get caught more often because your gaurd is not up.. Also by having your hands down and not up your loosing punching power..
By bringing shots up from your hip you arent getting any snap in your shots and just putting your arm out there..Doesnt matter how fast you push the shot out its more like a poke with the glove or sometimes a backhand throwing the jab out there.. Plus when you finish punching your arm will go back down and your completely open for counters when you least expect it..Which just means the punches are just going to hurt more...

You'll eventually realise that fighting the way the trainer is telling you will benefit you in the long run and get you into good habits..Then once you have experiance under your belt.. Then you can build on your style.. But until then Just keep it nice and simple and keep your hands up..
Good luck..
Peace