Why do marx and engels believe that the capitalist system is doomed

First thing to know is that both Marx and Engels thought that the socialist system was perfect. And it was, in theory. Former Yugoslavia was one respected by the West and the East countrys.
The socialist system had the idea of public gain and public lose. Everything was public (but controlled by the country) both losses and gains. But in practice it was different.
The capitalist system idea was based on personal gain and personal lose. You had what you earned, and it was yours. Whether that was high lose or high gain it was controlled by you, not yhe country.
Now this is all in theory. Both systems failed because no theory or idea can be put to practice perfectly.

Now to answer your question. They believed the capitalist system would fail because everyone was working for their personal gain. Unlike the socialist system where everyone worked for the good of the public.

Hope you are satisfied with the answer. ;)

P.S. I know the answer is long, but I like to explane where my answer comes from.

What he said

Each mans success depends on his own hard work