Logic is subjective yes, but it differs from feeling, at least how "feeling" is understood by most, in that logic attempts a sort of impartiality. It seperates the process of feeling, or sensing, from the feeling or senses themselves, and emphasizes the process, looking for consistency. Personal logic is nothing more than a process of logic that has yet to be identified as occuring outside of ourselves, and therefore limited in scope in it's practical ability in the real world. It's why many Ti users deem feeling as inferior, because they want to prove that their process of feeling is correct and they do that by looking to see if their process of feeling has occured in others. If it hasn't they conclude that the process of feeling that led to that feeling was flawed, and therefoe the feeling is wrong, which, ironically is illogical.
Logic is subjective when two parties don't agree agree..and objective when two parties do agree. Another way if saying this is..two people's subjective logic becomes objective logic (outside of those two people) when both agree that that is the case. "Logic" as is commonly understood, is simply the extrapolation of this to as many people as possible. This is why people disagree as to what exactly is logical, because anything can be assumed to be logical given the right persons.
Logic scales to people.