Why is the quantity of sentences not finite?

I'm currently studying formal languages. My lecture states that, while the words of a language are finite, the sentences build with the underlying grammar are not. But I don't get why this should be generally true. I can imagine grammar which leaves me with a finite amount of sentences.

I agree that one could create a language with infinite amount of sentences but I can't see why it should be generally the case.

Before I can tell you why there are arbitrarily long sentences in English, I would like to point out that 1 is a number,
2 is a number,
3 is a number,
4 is a number,
5 is a number,
6 is a number,
7 is a number,
8 is a number,
9 is a number,
10 is a number,
11 is a number,
12 is a number,
13 is a number,
14 is a number,
15 is a number,
16 is a number,
17 is a number,
18 is a number,
19 is a number,
20 is a number,
21 is a number,
22 is a number,
23 is a number,
24 is a number,
25 is a number,
26 is a number,
27 is a number,
28 is a number,
29 is a number,
30 is a number,
31 is a number,
32 is a number,
33 is a number,
34 is a number,
35 is a number,
36 is a number,
37 is a number,
38 is a number,
39 is a number,
40 is a number,
41 is a number, and
42 is a number. Of course, one could also think of other thing to point out, for example, that the son of the
son of the
son of the
son of the
son of the
son of the
son of the
son of the
son of my
son is my
grand
grand
grand
grand
grand
grand
grand
grand
grand
son. I hope I did not make a mistake there, or two mistakes, or three mistakes, or four mistakes, or five mistakes, or six mistakes, or seven mistakes. Let us stop there, as 7 is a nice number.

Do you still think that there is a bound on the length of grammatically correct English sentences?

StackExchange Computer Science Q#70847, answer score: 32