“The last thing I want is for you to feel like you can't open up to me about this kind of stuff.”

Your teenage daughter is starting to go on dates. She hasn't been talking to you much about it. You kept asking her about it, and she finally told you about some trouble she's having with a boy that she likes. You don't want her to feel embarrassed about talking about this topic with you, so you say:

The last thing I want is for you to feel like you can't open up to me about this kind of stuff.

the last thing I want is for (something) to (do something)

Use this expression to talk about something that you don't want. 

You tell someone "The last thing I want is for..." when you want to make sure that they don't misunderstand you. In the example above, the speaker is worried that the daughter thinks that she can't talk about her love life with her parents.

You can also say "The last thing I want is to (do something):

The last thing I want is to cause an argument on your birthday, but this is a serious problem.

open up to (someone) about (a topic)

To "open up to" someone means to tell them your personal thoughts.

"Opening up" usually means that you tell someone an emotional story or a secret about your life. English speakers think of "opening up" as a good thing. It's something that you're supposed to do in order to deal with problems in your life.

People that you can "open up to" include:

• a family member
• a friend
• a counselor

stuff

"Stuff" can mean almost any physical items or material. It's similar to the word "things", but "things" are countable and "stuff" is not. 

There's a good chance that you'll end up buying a lot of stuff while you're there.

Excuse me. Would you mind watching over my stuff for me for just a minute?

But "stuff" can also mean "topics" or "ideas", as in the example above. Here's another example:

We have a lot of stuff to talk about.