there are some things you can do that can sometimes help your veins suck less (drink lots of water, avoid things that dehydrate you or make you pee more like coffee/tea, be warm, move around a little before you do it to get your blood pumping)* but at the end of the day, some phlebotomists suck and some people just have shitty veins. I was really good at it and I definitely still had folks I'd struggle with, but if it's happened to you every time, I'd guess you've probably got shitty veins on top of whatever skill your stabbers have or haven't got
sorry, buddy.
and you're totally right to refuse that; while the gloves aren't sterile and are *mostly* about protecting the wearer, they're very likely to be significantly cleaner than their hands (which should be washed every time but they're not, like, Scrubbed In™)
* side note, one thing you DON'T want to do in this situation is have the tourniquet on for a long time and/or pump or squeeze your fist excessively. while this can increase the pressure and therefore make the veins more tumescent, it can lead to falsely elevated test results. the way this works is kind of like if you think about stuffing a bunch of wet clumpy mud into a stocking - if you squeeze it, the liquid can ooze out between the stocking mesh but the dirt particles cannot escape as easily, so a sample from a squozed as fuck stocking will yield much higher dirt content in relation to the whole than an unsquoze one.