What qualities of a leader make them inspirational and trustworthy? Why?

Someone who's able to connect by being actually honest with their dialog. Who also creates a vision for the future that is better than the present. Who manages people and doesn't manage tasks. For instance, when they give people objectives to take on they find out what they would like and then tailor things so they can perform. Actually working with their schedules and giving them mentorship or opportunities.

(because my why is:)
I think if they put some effort forward to make it about people first that lets me see something I can work towards and I trust a relationship where both people get what they want.

It's them taking the effort to find out what you want and go that direction.

One that doesn't lie at every chance like Hillary Clinton.

Bearing the responsibility .. It creates trust ..

https://youtu.be/XSRUmRYrRLY

Forcing transgender bathroom issues into the public forum.

Perverts matter.

Inspiring others to do the same

I would say that every now and then what they are saying has to be proven true.

It doesn't have to be a 100% success rate but they do have to vindicate themselves at regular intervals or the trust kinda dissipates.