For some people an interest in logic just seems to come naturally, and I think their natural talent tends to elide little things about it. If you're like me, innately bad at and uninterested in logic, you're left wondering if you're the only one to whom those things appear odd.
I've started learning about logic only recently, after being way more into continental philosophy. My main interest is in the epistemological status of logic. One of the things that always drove me insane in trying to understand it is that logicians and analytic philosophers tend to take logic so much for granted that they just assume it's synonymous with "philosophy" in any meaningful sense. But that really isn't the case.
The best way to understand it (openly admitting my bias) is historically, understanding what contexts gave rise to it and how and why people came to feel that it was a sovereign source of sure knowledge. The problem is that analytics also fucking hate historical approaches to philosophy. Aside from a few exceptions, and even they are minor, analytic philosophy has been extremely ahistorical. Even postpositvist analytics still wouldn't like what I'm saying here. But trust me, if you're not natively inclined to logical and mathematical thinking, and if one of your first instincts about mathematical reasoning is to question is epistemological and ontological status, you are really going to want to take an historical approach, and carefully suspend your judgement about whether logic really is the ideal form of philosophical discourse.
I would recommend you read histories of logic itself, like Kneale, but also auxiliary books like _Before Logic_ and general historical treatments of the genesis and epistemological-ontological status of Aristotelian, medieval, and pre-Fregean logic. Hair-splitting aside, Frege (or at least the movement Frege) represents is a decisive break in logic's self-conception. The birth of logic in the sense of analytic philosophy of out certain neo-Kantian and positivistic strains in the late 19th century is extremely different from what Kant meant by logic.
Almost no practitioner will tell you exactly how, though. Again, if you're continentally inclined, your first questions will be things like 'what did Kant mean by logic, and why? How did Frege formulate his conceptions? How does modern logic rest on Frege and Russell? What are the underlying epistemological and ontological assumptions about the access of logic to 'reality' in philosophers like Russell?" And so on. No one will answer this shit. They'll say: Kant was wrong and/or dumb, Frege was good, but now we've really figured it out, so shut the fuck up and get cracking on this or that 2000s logic textbook.
If things like defeasible reasoning through you I would really advise you to look into the stuff I recommended. Check out Heidegger's critique of logic as logos vs. aletheia, and Wittgenstein's critique of logicism in "the hardness of the logical must."