Honestly, I didn't thought this would be a hard question to answer, but I was surprised, I'll try my best but keep in mind English isn't my first language, so some weird grammar stuff might happen :p
In a blunt way, Marx had problems with the poetry Tupper wrote, it's a direct contrast of Marx's moral criticism in his works, but in order to truly grasp this, you would need to read at least some poems made by Tupper (assuming you never read them) and then be familiar with Marx's criticism of morality, it's difficult, there is not a clear answer like "oh he hated him because of this", so we need to search a bit further down.
Jeremy Bentham, another man Marx's had issues with, a philosopher who also shared some point of views with Marx, but ultimately the two are different in their approach; Marx says this about him on the first chapter of Das Kapital (if I'm not mistaken)
"Classical economy always loved to conceive social capital as a fixed magnitude of a
fixed degree of efficiency. But this prejudice was first established as a dogma by the
arch-Philistine, Jeremy Bentham, that insipid, pedantic, leather-tongued oracle of the
ordinary bourgeois intelligence of the 19th century."
Again, in a blunt way, one can analyze Bentham as a Reformer and Marx as the Radical, this is a simplistic view of course, but serves the purpose to answer the question. Now let me provide a bit of thought about Martin Tupper.
"To know what is useful for a dog, one must study dog-nature. This nature itself is
not to be deduced from the principle of utility. Applying this to man, he that would
criticize all human acts, movements, relations, etc., by the principle of utility, must
first deal with human nature in general, and then with human nature as modified in
each historical epoch. Bentham makes short work of it. With the driest naivete he
takes the modern shopkeeper . .. as the normal man. Whatever is useful to this
queer normal man, and to his world, is absolutely useful.... The Christian religion
e.g., is "useful," "because it forbids in the name of religion the same faults that the
penal code condemns in the name of the law." Artistic criticism is "harmful"
because it disturbs worthy people in their enjoyment of Martin Tupper"
There is a lot to digest here I know, but Marx critique of Tupper's works are basically about his morality, that Christian-Conservative world view that goes directly against Marx, you know, that Victorian period view of the man being extremely righteous and uphold reason above all else? Something like this, to understand Tupper's views on morality, I recommend reading his most famous work Proverbial Philosophy, it's an old book, it's boring, but hey, it might elucidate some mudded things in this.
Oh, some of the sources are not in English, but these are everything you'll need to go in-depth into this answer, I apologize if my answer does not satisfy your curiosity about this topic.
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