Learn Hardcore Latin: Pater dicit talem rumorem saepe falsum esse. - Father says that such a rumor is often false.

Because Latin uses a special construction after verbs of saying, thinking, knowing, hearing, and so on: the accusative-and-infinitive construction, often called indirect statement.

So after dicit (says), Latin does not normally use a finite verb with that. Instead, it puts:

the subject of the reported statement in the accusative
the verb of the reported statement in the infinitive

So in:

Pater dicit talem rumorem saepe falsum esse

the reported statement is basically:

Such a rumor is often false.

But once it becomes indirect after dicit, rumor becomes rumorem and est becomes esse.

Why is the verb esse an infinitive instead of est?

For the same reason: this is an indirect statement.

English usually says:

Father says that such a rumor is often false.

Latin usually says:

Father says such a rumor to be often false.

That sounds unnatural in English, but it is the normal Latin pattern. So:

est = is in a direct statement
esse = to be in an indirect statement

A direct version would be:

Talis rumor saepe falsus est.=