Many people breathe only into the upper chest and not the lower. This is not good practice because it hinders oxygen intake. It doesn’t bring in as much oxygen as your body can take in, nor as much as you need.
It’s not the only kind of breathing we have, especially if you’re a beginning tai chi practitioner. Breathe abdominally to ensure the lower lung fills with oxygen. Don’t think you have to hinder (upper) chest movement to breathe abdominally. If you do that, you’ll clamp down on the lungs when you want full, complete movement of the whole lung, ribs, sternum and even the lower and upper back. Once the lower lung fills, let your upper lung open and take in as much as the lower.
Abdominal breathing helps to lower the center of gravity, which is a good thing in tai chi practice. Filling the whole lung, chest, and ribs improve posture as well as allows more oxygen to enter, which is a good thing whatever you may be doing.