Certainly because it is a formality when two people introduce themselves, they shake hands as an introduction and it can also mean something positive, a strong handshake when there is a successful business closing. However, it is not the only connotation that can be given to this particular physical contact, such as squeezing hands.
In fact, there are people who just by obligation give their hand to another person, this is because for some reason they do not like to do it and while they can avoid it, the better for them. On the other hand, it is only part of being polite and respectful, especially so as not to leave anyone with an outstretched hand, it is also something that can be very fast depending on the occasion.
Personally, when I want to show my support to a loved one or special person, who is at an important moment in their life; I usually take his hand and hold it tight so he knows, I'm there and I'm with him. To calm the nerves and encourage him to do that if he can with that and more. I often do it with my daughters, when they have a school presentation and they are calmer.
Also when someone is going through difficult situations, it is the right time to say that you are there without saying words, with just a handshake.