Thank you for a civil and intelligent dialogue. It is better than the ego-laden insults that some fling out.
To address your thoughts, in general we seem to have a different value judgment about impermanence. You are not making a complete dismissal of thoughts as some others do, but there still in your thinking a tendency to downplay their importance because of their intangible nature.
Like some ancient Greek philosophers, some Buddhist thinkers (and nonthinkers) dismiss creations of the mind (thoughts) because they seem transitory and changing. It is the ancient prejudice that only things that are unchanging and permanent are real. But as I have said to others in this comments section, that thoughts are fleeting does not make them unreal. No, not all schools of Buddhist thought make the mistake of declaring all thoughts are illusions, but some do and I was responding to that.
Interestingly, the quote you reference from the Dhammapada proves my argument. We become what we think, exactly. Now, what does original Buddhism then do with that? It claims that it is our continued thinking/grasping that keeps us within Saṃsāra. It then says we should eliminate our thoughts so that we can eliminate our selves. Read Nāgārjuna on this issue, who expresses the thought well. Blow out the flame of your thoughts and be released from this world. This line of reasoning rests on the reality that we become what we think. Exactly the position I defend, but I celebrate that while Buddhism tries to negate this reality.
That desire for elimination of the self, to reach the state of No Self, is the motivation for Buddhism to state that all thoughts are illusions. Again, convince yourself that your thoughts are illusions, reject the illusion, and be released from the world. That thinking rests on the reality that we become what we think, which they twist into our thoughts are illusions, we are what we think, therefore, we are illusions. It has the appearance of logic, but a logical argument does not prove a reality. Neither does the thinking that we can negate ourselves by negating our thoughts. (and again, as I said, the contradiction of thinking one's thoughts are illusions....)
But as I ask in the article, why would people try to convince others to want to negate their thoughts and by extension (we become what we think, remember?) negate themselves? Such thoughts cause suffering, they do not alleviate suffering.