You don't give any context about why people might feel humiliated, besides you mentioning that they are high skilled specialists, so I'll add two things that could cause this kind of behavior from the little information you provided.
The first is if your daily standup is in fact just a status report to management. Someone from management participates in this meeting and criticizes people for no reason whatsoever than to exert their power and show who is boss. You have a manager of some sort that threats people like children, asking them what they did yesterday, what they will do today, making them promise to do it, then ask people to explain themselves if something doesn't go according to what everyone committed to do. Highly skilled professionals don't like these sort of things because they know it's a very moronic way of doing things. But they don't feel humiliated, they simply start being resentful in wchich case they will either try to do something to change things for the better or will leave and find a better job some place else where people are not such idiots. And they will find it easy to find another job because they are very skilled.
Do you have such a type of daily stand up? Most likely not. This is an extreme depiction of how a standup can take place. Which gets me to the second reason people might behave like you describe.
The second reason is overinflated egos. Do these developers have a bad attitude or not? Are they decent people or are they jerks? The daily standup has a purpose and that is for everyone in the team to coordinate their working efforts for reaching the goals of the Sprint. People should not feel humiliated unless the daily is messed up in some way (see the first reason I mentioned) or they feel that this is beneath them. Being very skilled doesn't mean they are also professionals. In a Scrum team people need to collaborate, understand the role of a daily, and act professionally. If you don't have such persons in your team, you are in big trouble and them considering it humiliating is the least of your problems.