Why must I have the other party's consent to record a phone call?

You're talking to ME. You called MY line, which is basically MY property. Not yours. So why shouldn't I be legally allowed to record the conversation?

Well, whatever the other person is talking to you are his/her own thoughts and words, and not yours. So you are actually recording his/her thoughts/words. Naturally you should ask for his/her permission.

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Not sure of the law in the US but over here you're freely allowed to record the conversation. You're not allowed to the publish the recording without the individual's consent and it's inadmissable as evidence in a dispute without it but the actual act of recording is fine.

yeh i dont see what the problem is. I would imagine US law would be the same (any US citizens here who could clarify?), record as much as you like, you only problem is if you want to use those recordings.

Most states require one party in a conversation to allow the recording - which means, in those states, you do not need to notify others that you are recording the conversation.

Rather than use the phrase 'legally': you should instead note that it is not prohibited by law (the caveat being a state issue). There IS a difference.

Additionally, you are not directly prohibited from publishing said conversation, however, other laws may come into play when doing so (e.g. interfering with an investigation, secrecy, and possibly slander). It may open oneself to civil suit, even if you have not been legally prohibited from publishing said conversation.

The rules on recording differs from state to state, as I understand it. Perhaps ALL states are as SJWhiteley stated. The ones I am sure about are, though I also have some memory of being in a state where you weren't allowed to record a conversation without consent of all involved. Still, that consent thing may be like the law prohibiting driving barefoot: There isn't one in any state, but lots of people think there is.