I'm not missing your point. I've consistently addressed your arguments.
Yes, it is certainly the case that certain arts disciplines deal with compassion. But then so do certain science disciplines. I would certainly expect some computer scientists working with AI and robotics to have more academic expertise on the nature of compassion and empathy than say, someone studying the History of trade arrangements, because the former may be attempting to create something that can learn about and respond appropriately to human emotions while the latter may be analysing large scale systems.
Either way, I see no evidence that the huge increase over the last twenty years in students doing arts degrees has created a society that is more caring, compassionate or prone to sharing.
And all disciplines involve working with people.
Nobody has argued that arts disciplines are of less value. English Literature, History, Classics, Acting, Philosophy and so on are obviously vital and some people should pursue them. The issue is the numbers of girls not going into STEM, who may be doing arts degrees instead. Presumably you must agree that there must be some number of people who do STEM, and at some point, say if 99, 93 or whatever percent of people decided to do an arts degree, you'd agree we had a STEM shortage. I, and many others, including the government think we've already reached the point now where we have a STEM shortage.
To answer your question about why the low numbers of women in STEM will mean that women are left behind culturally, politically and economically...
We are a technological species. Technology had already been invented before our species evolved. We have never existed without using technology to interact with our environment and survive.
The technology we are using in our current society is highly complex and pervasive. Without an understanding of what it is, how it works, how it changes environments and societies and the ethical questions around that, people cannot contribute to discussion in an informed way about the political, cultural, social and economic future.
They will be left behind.
Except of course we're trying to stop that, for a start by increasing the amount of STEM girls are exposed to long before they get to 14 and start picking options. Because it is fundamental to democracy that everyone is educated about the world we live in.
I also note that various posters from science backgrounds are on here using a range of rational discussion skills and arguments which are the subject matter of the arts - particularly philosophy and politics. Because scientists understand that the arts matter and knowledge and skills from them must be developed post sixteen. But unfortunately, many people fail to develop much knowledge and skills of STEM post sixteen, and that needs to change.