Well, you have a lot of arguments in favor of boost:
If your boss argue that can't use because licensing issues, you could copy the Boost license, which is really clear and objective, and ask where ?
If he say that is hard to find people that understand STL, and even harder for boost, you could say that he is probally right, but, is much more easier to learn Boost than STL, even more, Boost documentation is extremelly good, and have a lot of examples. Boost is much more easy to learn than lot of libraries like MFC, ATL, STL, QT. So, you could argue that anyone that knows MFC, ATL, STL or QT, would be able to get into boost fast.
If he say that boost is not standardise, ask him to look the boost code. All the code follows the same guideline, same guidelines of stl. Even more, majoraty of boost commitee members are also part of the C++ standard. And the TR1 is implemented in the boost.
If he say that is difficult to distribute boost or they have to ensure that the client has the right version, you could just say that you would use "bcp" tool. BCP is a boost tool, used to copy all the boost dependent code direct to your application, so, your application would use only the boost files that uses.
If he say that boost would take a long way to learn, you could say that boost would save a lot of time avoiding you to reinvent the wheel. And boost is really dificult to use in wrong way, so, it forces the code quality to be good.
I would probably not ask if I can use BOOST, I would just simple use it. I did that a lot of times, and people that I knew that would be against it, liked it after, first because the could understand the code, and the quality was high because the usage of boost unit tests, and there was nearly none bugs.
But, in you case your boss already told NO. He probably doesn't know how to program computers, but you could try make a deal, like, use only boost libraries that are in TR1, and not using the boost namespace, using the std::tr1 namespace. It will be in next c++ standard anyway. And If he says no, you could simple use BCP, to copy the headers to your application directory, and use as std::tr1 in your code, and tell him that you are using only the boost tr1 implementation, and if he doesn't like, he could buy a tr1, or even better, ask him to let you develop all the classes in tr1, it would take a long time to you, but for sure, would be a lot fun :)
You learned a lesson, don't ASK, USE IT. People are usual afraid of what they don't know.