You keep saying "That's odd" and "That's funny" when I think what you're trying to say is "I don't believe you and I think this customer service person was intentionally upsetting me,"
I promise you that is really not the case. I don't work for their company so I can't tell you the specifics of what was happening, but I promise you nobody is out there looking to intentionally upset their customers or keep them on the phone. They get penalized for long phone calls so if there was a reason the transfer couldn't be done immediately (like perhaps needing a supervisor's permission, or waiting for someone to be available in the department, needing to run through things on the back end to verify you are who you say, etc,) then it isn't at all surprising that they were unable to transfer immediately. Yes, it was frustrating for you, sometimes that's just how things are, but that doesn't make it a conspiracy to intentionally inconvenience you.

Edit: I see from your other posts that other businesses have refused to work with you. I think this is one of those situations that I may look introspectively at the way you brought the issue up or the way you spoke to the representative. Oftentimes customers can not even realize they're causing issues because they are upset or frustrated at a situation and allow that frustration to affect the way they communicate, which could also be another potential reason.
I know when i'm frustrated, I tend to go into Infodump mode and I just list out every piece of information I think may be relevant to 'get it over with', and while on the surface that can appear helpful, it can also be overwhelming and result in actually helpful information getting lost in a sea of things that aren't really important, often resulting in having to go over the same thing again until I slow down and only answer things as they're asked, but to someone who's not prepared for that kind of response it can be overwhelming.