The Order of Combat
The Player’s Handbook lays out the Order of Combat in three steps: determine surprise, establish positions, then roll initiative. That initiative roll, a Dexterity check, decides the sequence. High to low, everyone takes a turn, then you repeat. The word people trip over is “Dexterity check.” They read it as “the Dexterity guy goes first,” which is not what the rule says.
Your Dexterity modifier feeds the roll. It does not override it. A d20 has twenty faces, and a nimble rogue can roll a 3 while the plate-armored fighter rolls a 19. The fighter acts first that combat, and nothing about the rules is offended by this. Movement speed does not enter the calculation at all. Speed governs how far you travel on your turn, not when your turn arrives.
The confusion usually surfaces when a slower character acts ahead of a faster one and someone at the table objects on principle. There is no principle. There is a number rolled at the start of the encounter, and it holds for the whole fight unless something changes it.
At the table: When a player argues their high-Dex character “should” go first, point at their initiative total, not their sheet, and proceed in descending order.
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