This question generates more confident disagreement among tilers than almost any other, which should tell you that both approaches work. What matters is that whichever is chosen is executed properly.
The case for floor first
Tiling the floor first gives you a continuous floor running to the walls, with the wall tiles finishing on top of it. The junction is clean and the bottom row of wall tiles hides the edge of the floor.
It also means the floor is not being measured to fit around wall tiles that are not there yet, and it avoids a situation where the wall tiles finish at a level the floor then has to meet exactly.
The obvious risk is damage. A newly tiled floor is walked on, has ladders and trestles stood on it, and has adhesive and grout dropped on it while the walls are done. Protection is essential, and the floor needs its full curing time before anyone works off it.
The case for walls first
Working off a level batten fixed to the wall, the tiler sets the second row up and tiles the walls, leaving the bottom row until the floor is in.
The floor is then laid, and the final row of wall tiles is cut and fitted to meet it. Nothing heavy is done above a finished floor.
This is the traditional approach and it protects the more expensive and more easily damaged surface. Its weakness is that the bottom row of cuts has to be accurate, and if the floor is not level the cut row will taper visibly.
What actually matters
The junction between wall and floor is a movement joint. Walls and floors move independently, particularly on suspended timber floors in older properties, and the corner is where that movement concentrates.
That junction must be filled with a flexible silicone sealant, not grout. Grout there is rigid and will crack, and a cracked line at floor level in a shower is a direct path for water into the structure.
Getting this right matters far more than the order of work. A perfectly sequenced job with grout in the corner will fail; either sequence with a proper flexible joint will not.
Where the answer is clearer
In a wet room or a shower enclosure, the waterproofing dictates the sequence rather than preference. The tanking system has to be continuous across the wall-floor junction, and the manufacturer's detail for that junction determines the order. Follow it.
Where the floor is being built up with a backer board or decoupling membrane, that build-up needs to be in place before the wall tiling is set out, because it determines the finished floor level and therefore where the bottom row of wall tiles sits.
Setting out
Whichever order, setting out is what separates a good tiling job from a mediocre one.
A competent tiler will plan the layout so that cuts fall in inconspicuous places, that there is no sliver of a tile at a corner or at the top of a wall, and that the pattern is centred on the features that draw the eye.
Ask how they intend to set the room out before they start. A tiler who has thought about where the cuts land is a tiler who will produce a job you are happy with. One who starts in a corner and works along is not.