Most likely you've reached your manpower limit. (I'm a veteran Paradox games player though trying this original EU out now too and in the tutorial scenario reached my own manpower limit from building armies too).

To check this ingame on the main screen, look at the upper right and you'll see three sets of numbers to the right of the current date in the game. First is stability (generally +3 in the tutorial), then second is your manpower available (in thousands). If you move the cursor over that grey image of three men together by that number and wait for the tool-tip to display, it'll give you the number of your current troops and the maximum number that you're capable of. (in my game's current case, that's: 'You have a man power of 488,000 (Maximum is 504,000)'. It'll also give the rate at which you gain/regain manpower each year.

ADDED: Sorry, I posted this not noticing it's specifically cavalry and warships that it's not letting you build. That's the case for me in the tutorial as well, but with what manpower I have left it does still allow me to build infantry and transport ships. So unfortunately I'm afraid my suggestion isn't quite what we're looking for.

Thanks for that, looks like its disabled to make the tutorial simpler or just bugged.