It’s okay to be vulnerable
Almost all of us have wrestled with the fear that being vulnerable will push others away. We become embarrassed when we cry and apologize for having strong emotions. We even hesitate to talk too much about our family for fear of being awkward.
The irony is that when others open up a little, we are drawn to them. We don't feel disgusted when someone else has a strong emotional reaction or even cries. I've been in the room when executives in the same company finally talk about their kids after years of trying to impress each other by staying professional. The discovery that they had kids of similar ages and activities increased their appreciation for each other, not the opposite.
The more we know about a person, the more we trust them. Even knowing some of their struggles can increase trust. If you're bad with remembering details (or if you get stressed out obsessing over the details right before an event), don't pretend it's easy for you. Own it and ask for help. They will trust you more. (Oh, and they probably already know you struggle with that, by the way. )
And if you're the leader of that team, then the way you get your people to trust you is to model being vulnerable. Leaders go first, then ask others to follow.
You don't have to share all the intimate details of your life. That may be too soon. Work your way up to that if you ever get there. But share some simple things first and see what happens. You might be surprised at the response you get.