what am I missing regarding answering the telephone?

No. You know they are being rude by having no appreciation for your instructions: you answer the phone and take messages as appropriate. If someone is not available, you cannot make them so.

Some people think their wants override everything else and make demands you simply can't meet. Not your problem.

[I work in a doctor's office - he is *always* with a patient and unable to take calls, no matter who it is. They can leave messages with me or send him an email, but I don't even attempt putting calls through to him unless it's one of his children with a bonafide emergency. People don't like it, but his patients in his office come first. Always. I've had them stomp and snort with me on the phone demanding to talk to HIM, and it's turned out they just wanted to make an appointment or have questions about their insurance. He doesn't do that - I do. That's what he pays me for.]

People may have started getting too used to electronic voicemail. On our phones at work, there is this "do not disturb" feature where you can program in a message that goes something like "I'm sorry, I'm with a client, Please leave your name and number and I'll get back to you when I'm free." Or whatever other message you like given out when someone calls. There is also the regular phone message that will play if you don't use the "do not disturb" feature--which you set up in whatever words you want. If you don't want to answer your phone, if you've gone out to lunch, if you left to go fishing, whoever calls just automatically rolls to voice mail after X rings--there's no one to argue with (like a real person answering the phone) and no one for the caller to take out his/her anger on because it's all electronic. Oh, we have had callers who do get angry and will leave angry voice mail ("I've tried calling you 25 times and just get your voice mail. Don't you ever work? Blah blah..."), and sometimes the message gets transcribed (and a copy of the voice mail gets saved too) for future reference. But, in the bigger picture, I think people are just forgetting how to be courteous in general.

I don't think I would say, "He's already gone for the day," because it implies they are not important enough to speak with someone personally about their problem.

I generally teach my employees to say, "I'm sorry, he's busy at the moment but should be available shortly. If you'd like to leave a message, I'll see that he gets it. You should hear from him within (time frame)."

Nope. You're okay. It's just you've had the "luck" of encountering 3 very rude customers rather recently.

Have a polite day.

Etiquette takes over where laws end.

sounds like you are being more than accommodating. but this is the nature of call center work or answering phone's you inevitably have to deal with the public, and unfortunately a majority of the public are just outright demanding, inconsiderate, and selfish.

youre not missing anything, theyre just being rude