This is a line spoken by Jordan Baker to the narrator, Nick Carraway, after she had very nearly hit a workman with her car. In fact, she came so close that her "fender flicked a button on one man's coat." Jordan is not careful; on the contrary, she is rather careless herself, playing so fast and loose with another person's life. However, she doesn't want to change her own ways. Instead, she is attracted to people who are not like her, who will "keep out of [her] way." It is ironic that she claims not to like people who are like her yet logical at the same time. Jordan wants to be reckless and carefree, but when everyone is that way, chaos ensues. She seems to desire the freedom to be carefree, or "careless," without having to worry about chaos, as other people are being careful.
In telling Nick that this is why she likes him, she implies that, in their relationship, he will have to carry the burden of caring while she will prefer to be "careless." As long as he is watching out, paying attention, and staying out of her way, so to speak, everything will be fine, and their relationship will run smoothly. It really places an unfair amount of responsibility on him, to always be "watching out" for her, getting out of her way, always caring while she does not.