When Hashem went around offering the Torah to the other nations each asked what is written therein to each nation He told them of the commandment representing their weak point or vice, hence they rejected it. The question remains if you look at the things Hashem brought up they are all included in the Seven Commandments which Non Jews are responsible to keep even without the Torah. The question is why did Hashem choose to pick something they were already commanded in and why if they were commanded in these things anyway did they not accept?
The sefer Dor Revi'i answers that unscrupulous scholars are able to twist the Torah in any direction they choose, using the Torah against itself. Such as the Jewish king Menashe who was able to purify the Sheretz with 150 reasons. This was the reason the nations rejected it. They claimed that once the Torah was in their hands, they would find ample room to be lenient in prohibitions that they were especially susceptible to.
The gemara answers your question on Avodah Zara 2b. The reasons have to do with G-d's judgement at the end of days. If the nations defend themselves by saying to G-d 'If you had offered us the Torah as you offered it to Am Yisroel...' then that can be answered by saying that it was offered. If they defend themselves by saying to G-d 'If you had compelled us to accept the Torah as you compelled Am Yisroel...' then that can be answered by saying just as you didn't keep the Sheva Mitzvos B'nei Noach you wouldn't have kept the Torah either. As Yishayahu said (43:9) "and the first ones will inform us" (while talking about G-d's judgement of the world at the end of days). That is why mitzvos from the 7 Noachide laws are used here. The gemara explains all this in detail and I recommend you learn it inside.