The reasons why a suspension bridge was chosen over other designs were due to two key reasons:

First the Humber River has a shifting bed and is deep enough and wide enough to afford passage to ships, but that is always changing. A suspension bridge with no support piers within the river would not obstruct the estuary. 

Secondly, because of the local landscape a construction of a tunnel under the bridge would have been far more costly.

Many different ideas were put forward however over the years, mainly before the knowledge of the Humber had been gained.

Humber Bridge Design by Ralph Freeman