I wanted to make a few comments about why this article doesn't discuss using machines or bands to develop the pullup. And by that I really mean chinup since most people will do a chinup first.
1. The suggestions in this article are meant as an alternative to machine or bands and for those who:
a. Don't have access to a machine and
b. don't want to have to buy bands in order to do a pull up
2. These suggestions are meant to allow the trainee to immediately start handling his or her own body weight. Machine and bands change the feel and technique of the movement in several ways by putting a displacing force underneath the trainee.
3. Developing the exercise under your own steam gives one a psychological edge. The progress one gets when doing the supine rows and the various partials is encouraging and motivating…especially owing the the lack of "artificial aids". Never discount the mental aspect of this type of challenge.
4. The supine row itself is a great exercise so there is the benefit of doing a "real" strength training exercise and progressing on it right away.
5. There is no rule saying that these techniques cannot be combined with other ways…such as resistance bands and/or pullup assist machines. And this is certainly not about being a "purist". The goal is the get your first pullup. Whatever works is good as long as it doesn't cause harm. Many trainees will want to combine these techniques with other things and not only should they do so I hope they do…using your own head is always the best way to get things done.
Recognize that I explained thoroughly those practices I disagreed with and why before moving on to the plan for getting your first pullup. If I had disagreed with other things like bands and machines I would have put that in. I just don't want you to get hurt. That does not mean I want you to close your mind to other things that may work.
The Big Pink Elephant
I've been getting around to this and I don't want people to think I'm ignoring it. The article itself is meant to be encouraging but we have to contend with reality as well. You want to finally get that first pullup but you are significantly overweight. You may be fighting a losing battle as far as pullups go then. You will have to drop some of the excess body weight, pure and simple. That does NOT mean that meanwhile you cannot begin training toward the pullup, though! It is not a one or the other proposition.
What is a "significant" amount of excess body weight, in terms of pull ups, will vary among individuals because different trainees have different degrees of relative upper body strength. Not only that but some people can have a great deal of upper body "pulling" ability and be very average or poor in pressing strength. Or vice versa.
There are members of this site who can perform a pull up with 75 to 100 pounds of extra weight strapped to their body using a dip belt. But that does not mean they would have been able to achieve their first pull up if they were carrying around that extra 75 pounds. Because remember that before they could achieve the extra weight they first had to build reps and work tolerance with body weight and then incremental increases in additional weight in the form of plates.
Achieving the first pullup or chinup is going to be a different experience for everyone. While "how to do your first pullup" is the main question that trainees ask, "how long will it take" is the second one. And I wish I could give a good answer but there are no easily accessible rules. There are just too many variables. It may take you one month. It may take you six months. It may take a year. But probably not if you are dilligent (and you lose that extra fat).