Firstly, even as an ordinary owner, you would be entitled to see the building management agreement, or any other agreement, for that matter, but that would usually be via the strata manager.
Whether the building manager is required to let anyone see the management agreement directly is another matter, although you would think that the strata scheme secretary would be an obvious contender.
The simplest way to resolve this is to get the strata manager to show you the agreement, which you are entitled to see as part of your role as secretary.
Then you might want to look closely at why the building manager was reluctant to let you see it.