What is the word in Pali that is translated as being by some and as becoming by others? I'm referring to translations in accesstoinsight.org; what is the word in Pali that is translated as "being" by John D. Ireland and "becoming" by Thanissaro Bhikkhu? For example, in Itivuttaka: The Group of Twos -  49. Held by Views.  links and sample translations are given below.

John D. Ireland translation 


  "Bhikkhus, held by two kinds of views, some devas and human beings
  hold back and some overreach; only those with vision see.
  
  "And how, bhikkhus, do some hold back? Devas and humans enjoy being,
  delight in being, are satisfied with being. When Dhamma is taught to
  them for the cessation of being, their minds do not enter into it or
  acquire confidence in it or settle upon it or become resolved upon it.
  Thus, bhikkhus, do some hold back.


Thanissaro Bhikkhu translation 


  This was said by the Blessed One, said by the Arahant, so I have
  heard: "Overcome by two viewpoints, some human &amp; divine beings adhere,
  other human &amp; divine beings slip right past, while those with vision
  see.
  
  "And how do some adhere? Human &amp; divine beings enjoy becoming, delight
  in becoming, are satisfied with becoming. When the Dhamma is being
  taught for the sake of the cessation of becoming, their minds do not
  take to it, are not calmed by it, do not settle on it or become
  resolved on it. This is how some adhere.
The word is "bhava" and in my understanding it refers to a particular state of individualized existence: "being a living being", "being a human", "being a person". So it's not about just the mathematical fact of existence, it is about your subjective position of identifying with this particular organism and its personal story, its narrative.

So when Buddha says "devas and humans enjoy being", and "Dhamma is taught for the cessation of being" - it does not mean, Dhamma advocates death or annihilation, it advocates transcending identification with an individual living being.

Does not mean Dharma advocates identitying with Universe  either, that's another wrong view. Instead, the right view is to see the unhealthy outcomes of any and all identification and to abandon identification altogether.

P.S.

As @ChrisW noted, bhava is also notably mentioned in the Second Noble truth as classification of tanha (craving) into bhava-taṇhā and vibhava-taṇhā. In that context, again, bhava refers to a particular sate of existence - in this case a state of existence that we crave for: "I want to live in a certain way, I want to be X, I want to be surrounded by Y, I want my life to look like Z". Vibhava then refers to not being in a particular state: "I want to stop being poor, I want to stop being sick, I want to stop being lonely" etc.

In all cases bhava seems to always be connected with an idea of self in a broad sense - self not as subject of experience or agent of actions, but rather as one's state of existence.