When a girl says, "we should be friends" after meeting for the first time, it generally means that she is not interested in pursuing a romantic relationship with you but would like to maintain a platonic and friendly connection. In other words, she sees you as a potential friend rather than a romantic partner.
There could be several reasons why she might have said this:
No romantic interest: She may have felt no romantic spark or attraction during the initial meeting but still enjoyed your company and personality, leading her to suggest a friendship instead.
Wanting to take it slow: Some people prefer to start as friends to get to know each other better before considering a romantic relationship. This approach allows them to build a stronger foundation and assess compatibility.
Valuing friendship: She might prioritize building meaningful friendships and connections in her life, and suggesting friendship is a way of expressing this value.
Previous commitments: It's possible that she is already in a relationship or has other personal reasons that make her uninterested in dating at the moment.
Avoiding discomfort: Rather than directly rejecting you, some people might opt for the "let's be friends" approach to soften the rejection and avoid hurting your feelings.
It's essential to respect her feelings and decision. If you are genuinely interested in being friends, then accept the offer and nurture a friendship without expecting it to turn into a romantic relationship. However, if you were hoping for something more, it's okay to feel disappointed, but it's important to be gracious and understanding in your response.
Remember that everyone has different preferences and comfort levels when it comes to romantic relationships, and it's essential to communicate openly and honestly while respecting each other's boundaries. If you feel comfortable doing so, you can ask her for more clarity about her intentions to ensure you both are on the same page.