I'm vegan, I love it when people to take this approach. I went through the same process: I eliminated red meat first, then chicken, then fish, hung out for a while as vegetarian, then dropped honey/dairy, and then (hardest step) cheese before finally making the jump to full veganism. Currently trying to reduce cocoa, though I haven't completely eliminated it yet.
Part of what I like about people taking the more gradual approach is that I think they're much less likely to hit a wall and then go back to eating everything. Instead, every step of the process starts from a position of security/safety, and it ends up looking more like a person saying, "I'm comfortable not eating X, maybe I could also be comfortable not eating Y." And I think that makes things a lot less intimidating, and I think it makes it easier to build a different palete, and I think it means that each step is something that's small and surmountable rather than forcing you to build a substitute for every single food at once.
One thing I did as even a micro-step for some categories like dairy was to allow myself to order certain food at a restaurant but not buy it at a grocery store. You could also do the opposite -- depending on where you live, going vegetarian/vegan at restaurants is a good way of figuring out what alternative foods exist and what options you have for meat/dairy replacements.
And honestly, I also think this approach lines up somewhat well with veganism's overall philosophy, which is not about being in a position of moral superiority or about being perfect, it's about reducing harm. Going vegan doesn't mean none of your consumption contributes to suffering, it just reduces that number a bit. And the gradual process (on top of being (imo) easier to do and being less likely to result in backsliding to older habits) also kind of forces the person to live for a while in an uncomfortable place where they're trying to do better and aren't necessarily happy with their efforts or where they currently are. Again opinion me, but I think that's a good emotion for people to get used to if they become vegan; it guards against some of the tendency towards self-importance or pride that gets associated with veganism sometimes. I think it's good to be in a mindset of "X causes suffering, and independent of any other factor do I personally need to do X?"
Of course I'm hoping people go further than just reducing meat consumption, and I do hope that people don't take one step and say, "that's good enough, I don't need to ever think about this again." I also encourage taking tangible steps where you completely cut a food out rather than just reduce it, because "reducing" is a really fuzzy word that is easy to backslide on, and eliminating a food from a diet is a lot more tangible. But even if someone doesn't go any further or take those more tangible steps, reducing is still better than nothing. And I just think -- start with reducing, and see what happens. If you find out you can reduce, then maybe you can stretch a bit further and full-on eliminate that specific animal product, and then maybe you can stretch a bit further again and repeat the process with something else.
You get used to just looking around creatively at your life to see if there are small improvements to your consumption habits you can make, and then afterwards looking around again to see if there are new improvements you can make. I make vegan meals and enjoy certain vegetables now that I would not have had either the knowledge to pull off or the palete to enjoy when I started reducing meat. I think back to when I was getting rid of beef/pork, and there are literally foods that I didn't like back then that are now solid meat substitutes for me.