Is loving this girl with the intention of marriage forbidden, and why does society reject this love?

Love between the sexes is not forbidden in Sharia unless its causes and outcomes are unlawful. Sharia regulates love with two matters: The first is blocking unlawful means that give rise to love, such as mixing (of genders), looking (at the opposite sex with lust), and seclusion (with a non-mahram). The second is the consequences that result from it, where lovers must fear Allah and be chaste to avoid falling into unlawful acts. So, whoever finds love in their heart without an unlawful cause from them, and it does not lead to unlawful acts, is not to be blamed for it. Rather, they should strive towards marriage to preserve their faith and chastity.