In The Communist Manifesto, the two collaborators and philosophers Karl Marx and Friedrich Engels thought that the proletariat would inevitably defeat the bourgeoisie for two main reasons.

Before we get into those reasons, let's take a moment and define proletariat and bourgeoisie in the context of Marx and Engels. When they talk about the proletariat, they're referring to the working class. When they bring up the bourgeoisie, they're talking about the class that has most of society's money and control most of society’s shops, factories, or, as they’d say, “means of productions.”

The proletariat work for the bourgeoisie. The bourgeoisie are above the proletariat.

Now let's get into the two main reasons why Marx and Engels think that won't always be the case.

As work becomes more mechanized, they write, "the proletariat not only increases in number, it becomes concentrated in greater masses, its strength grows, and it feels that strength more."

The first main reason why Marx and Engels believe the proletariat will eventually topple the bourgeoisie is because the size of the working class will be overpowering. The size increases their strength, which the proletariat, according to Marx and Engels, "feels." They know they’re strong. Soon, they’ll show the bourgeoisie how strong they are.

The second main reason has to do with the nature of the bourgeoisie themselves. While Marks and Engels portray the proletariat as strong and united, they depict the bourgeoisie "in a constant battle." They're combating the aristocracy and they're competing with themselves. Their vulnerable, conflicted, and fragmented position leads to their eventual "decay" and to the rise of the stronger working class.

Marx and Engels thought of their theories as completely scientific, reflecting their faith in the rise of a new rationalistic, science-based age that had sprung fully into being by the nineteenth century.

In The Communist Manifesto, logic dictates that the proletariat victory is inevitable because the majority wins. Things of greater mass crush those of smaller mass. As they write:

The proletarian movement is the self-conscious, independent movement of the immense majority, in the interests of the immense majority.

While it is commonplace to see the proletariat as the factory workers, the uneducated, and those on the lowest rungs of society, to Marx and Engels, it was comprised of anyone who had to work for a living to survive economically. Anyway who was going to lose their home or have trouble paying their bills or buying food if they were out of work more than six months was a wage slave, a member of the proletariat—all the people who had no choice but to slog to the job everyday. This is what we today call the ninety-nine percent.

In the Manifesto, Marx and Engels point out that the capitalist class, the one percenters, need, according to the logic of capitalism, endlessly to expand their wealth. They need to find new markets, and to find new ways to wrest ever more money out of the workers. Since capitalism insists on limitless growth in a world that is inevitably limited, it will collapse from its own contradictions. Eventually, it will try to suck too much out of the proletariat, killing the goose that laid the golden egg. The proletariat class will finally, at that point, say "enough" and rebel. The working classes will inevitably win because they are the vast majority—the ninety-nine percent. If they decide to rise up (and "they" include the army and the police, the groups the capitalists depend on for protection), there is really nothing the capitalist class can do but accept defeat.

Marx and Engels believe that capitalism is unsustainable. As it develops, it will create an ever-growing army of poor proletarians, alienated from the products of their labor, and increasingly unable to benefit from the vast wealth which they create.

The antagonistic social relations that arise from capitalism can be suppressed by the ruling class for only so long; at some point, the proletariat, class-conscious and apprised of its role as the harbingers of historical change, will rise up and overthrow the capitalist system once and for all, leading the way towards a communist society.

Marx and Engels believe this process to be inevitable, because for them history is inevitable. In classical Marxist theory, history develops according to precise historical laws of change. In that sense, Marxism is held by its advocates to be scientific.

The proletariat is in the unique position that, as well as being subject to the forces of history, it also shapes those forces through the development of class-consciousness and through revolutionary action. Critics have seen this as a blatant contradiction. If communism is inevitable, then why is it necessary for the proletariat to develop class-consciousness and participate in revolutionary political activity? In other words, if something is inevitable, then surely there’s no need for the kind of action by the proletariat endorsed by Marx and Engels in The Communist Manifesto?

Marx and Engels believe that the victory of the proletariat over the bourgeoisie is inevitable for two related reasons.  First, they say that the capitalist system makes it impossible for the proletariat to continue to exist.  Second, they say that capitalism forces workers to come together and unite, thus ensuring that they will defeat the bourgeoisie.

First, the capitalist system makes it impossible for the proletariat to exist on its own without any help.  Marx and Engels say that the system creates a situation in which the worker

instead of rising with the progress of industry, sinks deeper and deeper below the conditions of existence of his own class.

This is not sustainable and will inevitably weaken capitalism.

Relatedly, capitalism forces workers to associate with one another, and thereby form a united front that will one day defeat capitalism.  Because capitalism exploits the proletariat so badly, it forces them to join together to try to resist.  They are no longer split up as individuals or small groups.  Instead, they eventually join together and come to understand how badly they are being exploited.  Since there are so many more workers than there are bourgeoisie, it is inevitable that a united working class will be able to overcome the bourgeoisie.  Therefore, the victory of the proletariat will inevitably occur.