Food habits of any group of people are a product of availability, physical environment and religious beliefs. In a coastal place like West Bengal where fish used to be available in abundance, the Brahmins of Bengal embraced fish eating given its availability, wide variety and taste.
I make some general observations about food habits of Bengali Brahmins, although they might differ on a case by case basis. Like I have mentioned earlier most Bengali Brahmins especially those residing in West Bengal are non-vegetarians and fish is a staple diet. In fact, traditionally fish is not considered non-vegetarian by them. Having said this there are pure vegetarian Brahmins who refrain from eating onion and garlic.
… According to brhadddharma purANa, the rohita (rui), shaphara (pu~Ti, shapharI), sakula (sola) etc. white fish with scales are allowed for brahmins. jImutavAhana mentions oil from illisa (ilisha, ilsA) as commonly used. However, fish that live in holes or in mud, fish whose head is shaped like a snake’s (e.g. vANa), those that look ugly and those that do not have scales were not allowed for the brahmins. Snails, crabs, chicken, crane, duck, dAtyUha (cAtaka), camel, cow, and pigs were considered inedible by the upper caste, though no doubt at least snails, crabs, chicken, and various kinds of proscribed fish and birds were eaten by the common people.
Chicken (and eggs of hen) was not popular and in fact is still not popular/ not consumed in many Bengali Brahmin families. The reason is historical and has to do with the fact that hen farms/ poultries were owned by Muslims and hence Hindus had religious reservations against consuming such items. However, in recent times chicken and eggs have come to be accepted unilaterally across all Bengalis.