The tattoo industry can be one of the most rewarding and lucrative careers, but getting your foot in the door at a good shop can seem impossible; you’ll face more doors slammed in your face and you'll hear “no” more than you'll receive the silence to speak. Many would-be tattoo artists refuse to listen to these rejections and choose the path of much criticism - learning at home. There are many pros and cons to both “traditional” apprenticeships and teaching yourself, but in an industry based entirely on talent, dedication, and art, there is no right versus wrong regardless of what traditional artists want you to believe.
The path you choose is the one that best suits your life and your personality type, but if you do it right and safe, no one way versus the the other will make you a better artist (this applies for learning to pierce as well).
Traditional apprenticeships are the societal norm and what tends to be perceived as better. The benefits are obvious - you learn faster and make less massive fuck ups. Having a professional hover over everything you do - from how you scrub tubes (if you even use tubes anymore!) to how you draw a tall ship, to how you tune your machine, how you apply stencils, how you clean the floor with a toothbrush (you can tell I come from a very traditional shop) - gives you a learning curve that may suck for the first few months or years till you're allowed to actually get some real needle in flesh practice. But when you do start, the trial and error that comes from teaching yourself doesn't exist.
In a traditional apprenticeship, you work for normally a year to three years for very little to no pay. You exchange grunt work and slave labor for knowledge and instruction, you leave with self-loathing and are often pushed to break by your mentor(s) in an attempt to make you prove you're worth it. If you have ever watched Karate Kid, nine times out of ten, you're doing something so irrelevant to tattooing that you truly wonder if you're ever going to get to hold a machine.
With a traditional apprenticeship, being young is your biggest ally. Once you have a family, rent or a mortgage, and have to provide, the nature of a traditional apprenticeship becomes too time consuming. However, you tend to become a stronger artist faster, you don’t need to be as self-motivated, and you don't need to be a very independent person who problem-solves and goes out of their way to achieve their goals. You have someone beside you, showing you the ropes and allowing you the safety of being in an already safe, sterile, and professional environment. When you work at a shop, they already have established suppliers and a reputation that allows prospective clients the comfort of just walking in and trusting that you are ready to tattoo them. A traditionally taught artist has a respect and love for their industry unmatched by anyone, because they had to earn their place through tears, sweat, and self doubt. In the shop, they tend to bleed tattooing as more than just tattooing - it is a lifestyle, and it is their identity.
The worst thing about learning the hard way is that it’s bloody fucking hard. You run into brick wall after brick wall; it’s long, frustrating, and plagued with skepticism; and regardless of how safe, sterile, and clean you are, the reputation of “kitchen magician” or “scratcher” will surround you for years, if you can escape it at all. You need to be smart, extremely determined, and hungry. You need to become a business owner and a highly successful one at that, as you need to convince people to trust you. You will jump through endless hoops to get supplies and make mistake after mistake just trying to find out how to pull a clean line. The positives now are that YouTube videos are plentiful and there are hundreds of books written to teach you the basics - there are even tattoo schools out there that can at the very least teach you how not to give someone HIV. Teaching yourself something will take you at least twice the time it takes a shop apprentice, just because they have guidance. If you walk into a shop as a home-based artist and ask for advice, you'll be laughed out the door, and Lord help you if you want to get into a reputable shop once you are a decent artist, as the reputation will haunt you till you become so good that people have no choice but to look past their preconceived ideas.
You are able to support your family by keeping a “real” job while you're learning and you can set your own schedule, which allows far more freedom than a traditional route. But you're also fighting against other home artists with ever dropping prices that come and go like high school girls going through friends, which makes it hard to charge enough to cover your hobby - which is exactly what it is while you're learning.
You'll find that you end up learning on yourself a lot and end up having legs covered in embarrassing terrible disasters, and you'll end up looking back at your old work with such despair and disbelief that someone actually let you butcher them with that monstrosity. But hey - you're an artist, and in the end, regardless on what medium you are working with, if you don't hate your art, then you're a douchebag.
In the end, there is no better or worse. There are only good shops and bad shops, good artists and bad artists, and if you're going to succeed, you have to start somewhere. If you're the type of person who thrives on other people, prefers being taught, likes feedback, is patient and a good listener, believes in respect and tradition, and is highly ambitious to become the best - I’d recommend the traditional path. But if you refuse to take no for an answer, if you are willing to fight day after day to learn, if you have a hunger that can only be satisfied by finishing what you start, if you're the type that makes their own path - then go the path of the most resistance and go with the knowledge that you are your only master.