Gonna take a moment to grandstand on this issue, as it's a pet peeve of mine.
The sayings in BJJ are vague and hard to interpret. There's a huge drive to leave ego at the door, don't bring ego on the mats, kill ego, etc. Many times we associate "ego" with "winning" or "caring about winning." Really, the intent (in my belief system) is that you shouldn't let ego inhibit your pursuit of technical excellence in all of grappling. In other words, if being afraid to lose is negatively impacting your ability to improve, then you need to "leave your ego at the door." I don't think it means you should roll like a wet noodle or just let people tap you for no reason. You should look to cultivate technique in your training partners as well (as ultimately, having better training partners will lead to you also having better technical expertise), and just handing out taps or giving pat-on-the-back rolls isn't going to help anyone improve their technique. Doing it as a motivator is one thing (though as I said previously, it failed in my experience), as keeping people coming back hungry for more will lead to an improvement in their technique. But doing it to prove you don't care don't improve technique at all. If anything, it's a bigger ego game ("I'm more humble than you!"). An apathetic approach to tapping/being tapped in training can be good, but it can also be bad. The deciding factor is whether or not it is improving your jiu jitsu.
Same analysis when people equate "using strength" with "ego", where people deride or chastise others for "muscling" things. The fact is using your strength correctly augments your performance and technique. If you use strength to the detriment or neglect of technique, then that's no good. That applies to your own technique (never learning how to properly do things because you wrench the arms of people half your size out of their socket like a caveman) or the technique of others (when I was 13 I had a grown adult power lifter bicep curl me when I was trying to armbar them; as a white belt it taught me not to trust armbars, which was counterproductive). However, learning to skillfully apply the strength you have is a "technique" in and of itself, so simply saying "no strength ever" is counter productive too. You may as well say no strength, no speed, no flexibility, no being taller or shorter than your opponent, no having different muscle fiber ratios to your opponent, no having a different personality from your opponent, and no having better abilities to learn than your opponent. You'd both just lay there like bricks, immobile, unmoving. It's madness. The "flow with the go" or "playing" rolls can be helpful to your technique, but they can also teach you to be lazy or to not capitalize on opportunities within the time frames they exist, which is detrimental to your technique too.
When you restate the focus to be improving your jiu jitsu (culmination of your physical attributes/abilities and mental attributes/abilities), everything else makes sense and falls into place. Of course it doesn't matter if you win or lose in training; all that matters is whether or not you're improving your technique. Of course you shouldn't hulk smash all the time if you aren't getting better; but the guy who is good that can also still extract his strength is a fucking beast. Of course you should sometimes "flow roll" if it is to the benefit of, rather than at the expense of, your technique.
Some people confound "improvement" with "taps" (sometimes improvement will lead to taps, but not always; and sometimes taps indicate improvement, but not always), but that's another issue. That's teaching people to identify improvement, and/or to learn how to learn, which is the difference between a great instructor and a mediocre instructor.
