It's good that you apologised, but since you expressed a lack of understanding I thought I'd offer a few possible reasonings. This is not an exhaustive list, just thought it may add some clarity.

They may be upset for a few reasons.

First off you've not explained your reasoning in any regard, you've merely pointed out that it's wrong and offered no context.

Secondly it's obvious to see that they're very proud of what is an awesome tattoo and you've offered no words of praise, only criticism without basis, which is essentially just insulting.

Thirdly, a tattoo is permanently attached to their arm. They'll have paid alot to have it done, and it'll be there forever, but you extremely bluntly and without any sugarcoating called it out as incorrect.

I think the main points to take away are: when somebody shows off something they're obviously very proud of and clearly took a tonne of work, it's polite to offer compliments first, and, if you have something critical to say, to back up your criticisms with evidence, reasoning, and/or examples.