Minimums exist because every job carries fixed setup work. In screen printing that means burning screens and setting up the press; in embroidery, digitizing and hooping; in cut and sew, fabric minimums from the mill, marker making, cutting and line setup. Spreading that work over more units keeps the cost of each piece reasonable.
MOQs are often counted per color or per style rather than per order, so three colorways can triple the requirement. Sizes within one color usually count toward the same minimum. DTG and other digital methods can go much lower because they need little or no setup.
When comparing suppliers, ask exactly how the minimum is counted and whether a smaller run is possible at a higher unit price. See MOQs and timelines and the screen printing cost guide.