Well, it could be shyness. Or they might be waiting for the room to quieten down. Making sure they remember the lyrics in that tricky verse. Trying to find a key that works. I've almost never sang at a singaround and I don't use sheet music or lyric sheets, but when called on to sing I often take a couple of minutes to choose a song that fits, remind myself of the lyrics, find a good key, (especially if I know someone else might come in with a harmony or there's backer and I don't want to force them into accompanying a song in f sharp minor or whatever) and so-on. Hopefully it's worth the wait. If it isn't then people should really stop asking me to sing.