Doesn't that vary a lot depending on what kind of law you practice?

At least for some kinds, there is a lot of non-adversarial human interaction. For example, in patent litigation you are usually part of a team and spend a lot of time working closely with the other lawyers on your side, paralegals, outside experts, inventors, and other people involved with the patent on your side.

Litigation is explicitly adversarial, and that includes many kinds of law that might seem "softer" at first blush. When you do housing law, you might spend a little time talking to an evicted old lady, but your real work is suing the landlord. Transactional is less overtly adversarial, but while the business guys are thinking about team synergies the lawyers are focusing on how the parties could try to screw each other if expectations don't pan out.

Lawyers work in teams, but programmers work in teams too. Having done both there is a lot more interactivity in programming teams (weekly status meetings, pair programming, dropping in on a neighbor to discuss APIs). (Legal teams are much smaller and cases are much less interconnected than large codebases).

E.g. teachers in India are 80% men. Source? My personal anecdote would be close to 50-50% with variance at higher college level and school level.

Teachers in India are nurturing?

Do men and women go equally into all fields which an attorney can practice in? As in, do corporate attorneys have the same gender ratio as family law attorneys? Do environmental attorneys have the same gender ratio as IP attorneys?

Law could be nurturing. There must be thousands of people that need legal help but can't afford it, or aren't in a position to seek it out even if they need it eg victim of abuse or assault.

In which case the attorney may double as a councillor of sorts.

This dual role is common in lots of jobs though. Maybe defending people is more appealing than maybe mentoring junior devs.

Maybe accounting is due to stability? In western countries you always need an accountant. You could probably make an argument about women not being risk takers.

Your last point is why statistics in developing countries are always brought up. At least one thing is clear, we can change the environment to get more women into STEM.

The 50% number applies to new large firm lawyers, not just "public interest" law. And your examples are unrealistic. Sexual assault victims don't get legal counsel. They might have (minimal) contact with the prosecutor, who is statistically likely to be a man. The accused rapist, meanwhile, might have (again, minimal) contact with a public defender, who is equally likely to be a man or woman. Both of those positions are primarily adversarial. Public defenders don't have time to nurture their clients--they try to get they are facts necessary to argue in court or negotiate a plea.