On the strategy map, when you drag a unit over a transport it should be highlighted and a green arched arrow shown on the mouse cursor.
If you mouse over the transport, what is listed for 'Cargo'? The transport may already be full, or unable to hold more of the type you are trying to load. A hunter takes up 2 spaces for example, so if you load a couple troopers and a couple grenadiers (giving a cargo of 4/5), a hunter will not fit (so there will be no green arrow, and dropping on the transport will result in hunters landing beside it).