Because you have to define it all from scratch (legally). Personhood has a lot of laws built around it as is.

The article notes several countries that have declared certain animals to be non-human persons, and the notion of corporate person is widely recognized.

If "we" refers to the USA, there isn't the political will to extend these rights to animals such as elephants or primates for many reasons (eg., Voter apathy, special interest groups that use animal testing, zoos, etc.).

Even if one sovereign decided to grant some animals personhood, that wouldn't necessarily be recognized outside that jurisdiction (e.g., two nations, state vs. federal govt.), so they would likely only be a "person" in specific contexts.

New laws require legislative acts, which are hard enough to get for uncontroversial things that a majority of people want.

The activists took the legal approach because there was potential to get the goal they wanted without legislation. A judge could have theoretically ruled that Happy constitutes a legal person, and was thus entitled to the protections afforded to legal persons. They didn't, but they could have.

I suspect that if not the activists involved in this example, some activists are working on getting legislation passed, but this probably seemed like a tactic worth trying as well.

Clearly corporations are people and deserve the same respect as humans.