It's either an ankle, hamstring, or hip flexibility/mobility issue. More than likely, assuming you're like everyone else who sits in a chair for work all day, it's shortened hamstrings and tight hip flexors. Try foam rolling your hip flexors and use static stretches on your hamstrings prior to lifting.
I can hit depth without doing all that, but I foam roll my IT band, hip flexors, glutes, and lower back, and then do seated hamstring, groin, and hip flexor stretches before I do my leg and back days. It makes a huge difference in how I feel when I squat. I just started doing some hip mobility stretches but haven't squatted since I started, but I imagine that'll help a ton too.
Here's the video for the hip mobility stuff. When I do it, I'm pretty much like the guy in the video. When I do the one leg, it's a freakishly noticable difference from the other.
And it's really depressing seeing other people squat. There are days when I see someone in there and they load up 315 and I'm like, "Fuck yes! Someone who can finally squat." And then I see them quarter squat and I just get sad. Worse than that though are the guys doing less than 225 with god awful form. Saw a guy the other day whose lower back was completely rounded. See lots of knees shooting in too. Also saw a guy doing 185 who failed, but instead of squatting lower and setting the bar on the safety rails, he just bent forward and dumped the weight over his head. My back hurt just watching it.