The character did dodge. The HP loss reflects this.
The Basic Rules defines Hit Points like this, on page 77:
Hit points represent a combination of physical and mental durability, the will to live, and luck. Creatures with
more hit points are more difficult to kill. Those with
fewer hit points are more fragile.
It expands on this with an aside at the top of the next page:
Describing the Effects of Damage
Dungeon Masters describe hit point loss in different ways.
When your current hit point total is half or more of your
hit point maximum, you typically show no signs of injury.
When you drop below half your hit point maximum, you
show signs of wear, such as cuts and bruises. An attack
that reduces you to 0 hit points strikes you directly, leaving
a bleeding injury or other trauma, or it simply knocks you
A successful attack isn't a sword actually slicing flesh. Combat experts are going to know how to avoid being hurt, but doing so takes effort which is in limited supply. Like Westley wearing out Inigo in The Princess Bride. There is no doubt that they both had successful attack rolls throughout the duel.
In this same way, your player's character successfully dodged the enemy's attack, but it took considerable effort to do so. That effort is reflected in a loss of HP. Clean and/or easy dodges that don't take effort are reflected in the character's AC, in the form of a Dexterity Bonus.
I recommend addressing these concerns via narration. Describe the way the character dodged or deflected the attack by the skin of their teeth, maybe leaving a slight cut on an arm or leg, when the attack hits them. And when the attack misses, describe how the character sees the attack coming and deftly steps aside. This has served me well with my tables of new players, who are more used to seeing their Skyrim character with arrows sticking out of them and are concerned about the long-term effects of taking damage. Eventually they'll become better adjusted to the mechanics and will no longer need such descriptions.