Hähnchen can be plural, but if you say "Du magst Hähnchen" you don't talk about the animal, but about the food, you wouldn't say "you like chickens" if you talk about the food. If you talk about the live animal you would say "Du magst Hühner" (female chicken) or "Du magst Hähne" (male chicken). In that case you would also use the plural form and say "chickens". You can use "Hähnchen" as plural if you talk about how many chickens a person ate. "Du hast zwei Hähnchen gegessen" "You ate two chickens".
I understand that I might say "I like hens" or "I like cockerels (male chickens)" but in English I am more likely to say "I like chickens" since I like this type of bird regardless of its gender. Are Germans more likely to say "Ich mag Huhner und Hähne" than "Ich mag Hänchen"?