Many of them charge cable operators for the right to carry them: https://en.wikipedia.org/wiki/Retransmission_consent - so having the channel available free online diminishes the value of the retransmission consent.
Also, the copyright licenses the station has for their programming usually specify limits on redistribution - e.g. geographical, types of carriage, amount of customers reached (with a wider distribution costing more, as it provides more value to the licensee and reduces the licensor's ability to sell licenses to other entities).
The cable operators are the only "broadband" ISP for most people in the US. Cable operators want income as both ISPs and as channel providers. The TV channels want income from cable operators and advertisers. Losing one means fewer avenues of revenue.
The reality is cable operators are no longer need to be anything but a dumb pipe. And TV channels are no longer as valuable as they once were due to multitude of other sources of information.
Also, the copyright licenses the station has for their programming usually specify limits on redistribution - e.g. geographical, types of carriage, amount of customers reached (with a wider distribution costing more, as it provides more value to the licensee and reduces the licensor's ability to sell licenses to other entities).