"Why must "to settle" be the main "acceptable" reason? Are all other arguments that weak?"

I think if we make the solar system a park- then we won't have any significant space development, until such time as we decide to allow people to live in Space. So, yeah all others are that weak.
A different way of saying this is if this places other than Earth in this solar system are places unsuitable for humans to live in, then NASA budget will be cut- we should spend more on Ocean exploration or tunnel boring.

The answer to question why are we doing space exploration is so that in the future there we be human settlements in space. The consequences of human settlements in space will be the delevopment of cheaper energy sources, the development of different human cultures, the expansion of science and our understanding of our world, our universe- new technology, and freedom.
Human settlement in space will change the minds of human beings living on Earth- it will change human awareness- it requires a change in human awareness and also changes human awareness.
It is an evolution- and may be an evolution that is rare in this galaxy.

If humans fail to go into space, it means without any doubt humans will go extinct- and all life on Earth will go extinct. This extinction probably going to happen before our sun goes nova, but it's a dead certainty when our Sun does turns into a red gaint. In timescale that we can vaguely grasp- centuries or even thousands of years, events which could cause human and/or life extinction which are exterior to Earth- Solar activity, impactors, other stars supernoving, or other changing conditions in our region of galaxic space, are unlikely sources of concern in regards to human extinction. BUT why assume that space development can't happen in within say next couple decade, but could in centuries or thousand years from now?
The danger in the near term is not extinction events, but rather events that disrupt the current civilization. These little are things like plagues, major earthquakes, super [or just big] volcanos, Great Depressions, a not so Little Ice Age, small impactor, a major war- tens of million per year killed for year after year, etc. This is not about the event it's about the political results from these events. The danger in near term is political and the events which could trigger this change. In terms human history, Iran is not strange- it's normal, America and the large number of democraies is the freak event- we are in a freedom, technology, democratic, socially progressive bubble.