I think sometimes it has to do with the person having a hard time with OT stuff. Homosexuality, women's place in the world, animal sacrifices, and God's punishments as their prophesied or recorded. All of those can be considered to be harsh topic in the OT. On that tone of thought, Jesus came to free us from all of that so Jusus must be against or partially against the OT.
Another way to come to that conclusion is confusing the old covenant with the laws, with the new covenant of Jesus's sacrifice for us. Without much else to go on from understanding the scriptures a person can conclude that Jesus takes us away from the old covenant, the OT, and thus is against both the old covenant and the OT.
With some study, or at least someone more knowledgeable about the bible teaching it, these things can be corrected.
It's also possible, since it was just a fragment of the conversation you caught, that the woman you overheard wasn't Christian. So like a person of a different religion, or an atheist, explaining about Christianity might come to the wrong conclusions, they might also have the wrong context to support their conclusions too.