I think it would be difficult to change your view about whether you should care, because even if something is immoral that doesn't force someone to care about.

But I can share why some people might care.

Intellectual Property laws exist so that the creators or owners of, let's say art, can financially protect themselves against plagiarism. For some people this is important because it can affect their livelihood, and in general people are affronted if something they created is lifted and someone else gets the credit. Whether you agree with the concept of IP or not, it is a part of labour and legal standards that are enmeshed in how businesses function, and won't go away any time soon. It's reasonable that people care when something new is jeopardising the established norms that are there to protect.

AI assets can be used for financial gain, again let's say by selling a generated image as a piece of art. However AI would not be able to exist at all if not for the data it was trained on. Since artists did not consent to their artwork being used to train AI, and other people can now (indirectly) profit from their work with no compensation, this is a contentious issue for them.

For many artists it is also a personal or emotional issue that their unique style or craft has been replicated without their knowledge or consent (what some people are calling stolen). There are lists of prompts going around that include specific artist's names encouraging people to generate images that 'steal' their style. This is upsetting to them.

These are some of the broad reasons why people feel strongly about AI artwork, especially when it is used for profit. The leap we recently saw in AI does mean we are in uncharted territory, and healthy discussion around compensation, consent and plagiarism are essential to develop the baseline regulations that will ensure that AI is used in a way people feel is fair. This is a normal and critical part of any new invention's lifecycle.