Here's the deal, you need to work this out with them as my post below is based entirely on the way I read a situation where I don't have all the facts. A less paranoid person might see nothing so alarming as the below.
Could you help me understand why the IT department would want to do this?
Well, this anwser is based mostly on supposition, as I can not think of any legitimate reasons.
They don't know how to route the public IPs properly or do not have the routed infrastructure to do so.
They think they know best and are applying their own security practices at the NAT level.
They find it easier to assign a public IP by DHCP than manually configuring and assigning one for each new tenant.
They take the BOFH handbook seriously.
What disadvantage is in it for me having it setup this way other then the inconvienience of not being able to use my external IP inside the building?
The option above that bothers me the most (and applies to your question) is that they might be deciding what traffic should and should not be passing.
It could be ports blocked, or SPI checks, or some level of IDS/IDP.
None of it belongs in a position where they can restrict your use of your connection.
Given they are performing NAT for you, some level of specific configuration had to go into these issues, they couldn't avoid having to touch on these subjects.
Best of all, they might not even be aware that they are doing it, and proving it will be annoying if they are defensive about it.
The other issue that came up is that they are telling me if my MAC address changes on my router, like plugging in a new device my internal Static IP would get's reassigned. Does this make any sense? Why would a static IP address ever drop my office as (i.e. router) no matter what I plug into it?
Are you pulling your internal static via DHCP? This is the option that falls into my theory of ineptitude and lack of ability or will to assign and configure statics. This would imply to me that they have a block of IPs and some static port forwards and are just letting anyone have any IP (this is not a public static).
If you had to manually assign this internal address then it sounds like they are trying to lock you down with ALGs, which points to them being competent, but less than ethical.