if you dont trust your own family in your own home. maybe you should get a divorce and get your kids sent away to be adopted.(joke)
My kids are young, I don't want them around when handling sensitive stuff because they're distracting.
I know that you were joking, but children can get you into trouble unintentionally. LoyceV mentioned one way that can happen. They distract you from your work because you have to pay attention that they don't fall down and injure themselves or they don't destroy something of value.
Let me give you another example. When kids get to a certain age, they start making up stories and innocent lies as their imagination starts running wild. What seems cute, can become troublesome. My friend's little pooper loves playing with me. We wrestle and he pushes me around and it's all fun. Recently, he has started "lying" and making up stories how other people hit him. Sounds cute? Maybe. It's not that cute being asked by the kindergarten teacher if you hit your children. That happened to my friend because his boy was letting his imagination run wild in front of everyone. He also told his teacher that his dad's friend (me) kicked him in the head and body-slammed him to the floor.

If your kids figure out that you are doing something on your computer with Bitcoin and money, that crazy imagination can come alive again and you never know who might be listening or be interested in their stories.
Andreas is using paper wallet to refer to "classic" paper wallets, which are a print out of a single private key and address, and I would agree that such wallets are outdated and expose the user to a number of unnecessary risks which I've talked about in a previous post.
And Andreas explained that in the beginning of his video. Because of that, he isn't wrong when he says that (single-key) paper wallets are obsolete and there are better ways to secure your Bitcoin.