In the Australia, UK, and other common law jurisdictions, you generally do not need to have a law degree, but you do have to do a short course that gives you the academic basics behind law - this can be and usually is done part-time, as an evening course and usually results in the award of a diploma. (see e.g. http://www.lawsociety.org.uk/law-careers/becoming-a-solicito... or http://www.lpab.justice.nsw.gov.au/Pages/lpab/legalprofessio...) While a good law degree helps get jobs, some of the best lawyers I have met used this path to get admitted to practice.
Being able to think like a lawyer is important, but the life of the law is common sense, experience and good judgment. That cannot be taught. Newly-qualified lawyers invariably tend to be up to speed on the theoretical aspects of law but cannot run a lawsuit, manage a deal or draft a contract to save themselves. What law school teaches (the basics of the subjects and thinking like a lawyer) is only about 1/10 to 1/20 of the role.
The real meat of the role is thinking strategically and pragmatically: yes, I can oppose this request, but what is it going to prompt the other side to do, and how will judge X take it when the matter is brought in front of him. In other words, what will the client possibly gain or lose from taking that course? Is it worth it? And what other courses are open? And what are they likely to lead to? What do I need to get to win the case, and what is optional, unnecessary or a distraction? How does this fit with what the client wants and (often) what the client needs that they don't even realise they need or (commonly) that they actively don't want to do? Good lawyers are thinking multiple steps down the road, not just the immediate problems, and have a good idea where they want to end up.
You can only get this by experience, and ideally by watching and learning from people who are experienced at it while they do it. You could try to do it by self-study, but you would likely be sued into oblivion by your clients for all the mistakes you would make (which would usually be caught and avoided by the more experienced person you should be learning under, and if not absorbed by their insurance). Based on my experience, which includes international experience, I estimate that you need 10 years of doing it full-time to be at a point where you would be able to describe yourself as competent, and able to do it alone, provided you have been working and learning during that time.
You need to learn human nature, how people think and are motivated, how they react to incentives and disincentives, and how they react to normative or moral issues. You need to appreciate that you never find black or white but only shades of grey. You need to learn ruthless pragmatism. You need to learn persuasion. You need to learn to recognise the gulf between what a contract or statute might say in black and white, versus what a judge will do when confronted with the practical justice of the contest. That difference is magnified if a jury is involved (don't get me started on the stupidities of the US jury system or the use of juries for anything other than criminal cases).
Law is much more a social science than it is anything else, but there is a big place for logic and logical thinking. Since you also need interpersonal skills, it is a hard discipline because you need to bring both "left" and "right" brain skills to bear.