Press secretaries also serve as a surrogate because the president is often too busy to answer all questions personally. I don't think that President Obama needed to hide behind a press secretary. There were a couple of times when a line of questioning would get to him, but he was able to maintain his calm despite the questions he got.

Trump is a narcissist and any question that isn't "positive" (doesn't specifically kiss his ass) is a direct attack on him. All of his press secretaries have exemplified his lying and aggression as well.