Most of us understand the issue of over-fishing (catching more fish than the ecosystem can naturally replenish) but perhaps not aware of the underlying issue of by-catch.
A lot of sea creatures are collateral damage in the fishing process (for example the classic WTO shrimp-turtle dispute case). As an average consumer, instead of stop eating seafood at all, a more effective action would be to pressure your government to regulate the fishing industry. Fishing nets and devices can be improved to minimize or prevent catching by-catch (e.g. a device that catch shrimp and allows turtle to escape in the WTO dispute case).