It's a complicated matter, and as a native speaker I'm lucky not to think about it consciously.
Typically, when a person is named after an inanimate object, the word behaves as if it were animate all along, so the option
Не хочу учить валенков / лаптей / чурок
is the correct one.
When it's the other way round, things get more complicated. I'd say ...
The real answer is the claim that "in principle all animate nouns are either masculine or feminine but cannot be neutral" is false. For instance, we consider obsolete yet existent word "дитё" (or "дитя") which is animate and neuter. Or "чадо", or "существо", or "чудовище" etc.
The situation is not unique to Russian, there's a famous example from German, a ...
Yes, this rule applies to animate nouns as well.
2/3/4 + старых/молодых + мужчины/мальчика/солдата for masculine or neuter.
2/3/4 + старые/молодые + женщины/девушки/кошки for feminine.
For feminine nouns you can also use the construction for masculine or neuter nouns (genitive plural) 2/3/4 + старых/молодых + женщины/девушки/кошки.
It won't be a mistake,...
A human language develops over time, and its rules often become counterintuitive. Whether you want it or not, even native speakers have to look into the dictionaries.
"Козёл", as a gymnastic tool, is a legitimate inanimate noun. Therefore "прыгать через козёл" is totally legit and even should be preferred. However, many people, including myself, have a ...
Usually noun in such usage just preserves the category it belongs "originally", so it's just
Я вижу всех твоих тараканов.
(since "таракан" is animate) - the same about "поставить на доску ската" - and
Не хочу учить валенки.
(since "валенки" is inanimate)
However I can not help but notice that, while grammatically, at least second phrase sounds ...