... I already explained that we do not lose fifty percent of our security at the halving, since the exchange rate also effects this dynamic ...
Not really. This year, we are paying roughly 10% of Bitcoin's total value, or what people here call "market cap," to secure it. In other words, we are currently spending roughly a dime to store (secure) a dollar for a year.
After the halvening, we will be paying only a nickel.
It doesn't matter how much a dollar is worth, the ratio remains the same.
Same for efficiency/cost of mining gear.
What matter is how much a Bitcoin is worth compared to fiat, since if the market capitalization of Bitcoin increases, the block reward will be worth more in terms of fiat value and real world purchasing power. This would stimulate increased mining since there will be profit to be made, since miners costs are still predominately in Fiat and it is the purchasing power of those Bitcoins that really matters not the amount of Bitcoins that are made. This is why the ratio does not stay the same, if the market cap of Bitcoins doubles so does the amount payed for security, these two things are explicitly linked.