Why does the apple store lie to my face about battery performance???

My phone battery use to last all day. Now it only makes it 3-4 hours with light use and in (low power mode).

I went into the Williamsburg, NY apple store to have the battery replaced and they ran some diagnostic test. I told them that I do not mind paying for the new battery and to preform the service regardless of what the diagnostic says. The test showed 300 cycles and 103% capacity. They said I don't need a new battery but they will sell me a new iphone 6 for $300. They argued that the diagnostic is correct and they will not do the service. If I need more capacity I should buy a case.

My phone also just shuts off at 7% if i try to open an app or make a phone call too. This does not seam like my battery is at 103%, not even close. I would estimate I am getting 20% of the battery life I use to get out of the phone when I first got it.

bout a year old. There is no reason for me to buy a new phone if I have a perfectly working phone with a battery that dies fast?? Does anyone else have this issue? Being told I don't know what I am talking about because they have diagnostic info on a screen is insulting.