I would preface this response to the two "logicians", that is, Miller and Highfield, with a paraphrased quote from Martin Niemoeller, a well respected Theologian, concerning the Nazi activity of the last century.

First, they came for the trade unionists and I did not object.
And they took them away.

Then they came for the homosexuals, and I did not object.
And they took them away.

Then they came for the Jews and I did not object.
And they took them away.

And then they came for me.
And there was no one left to object to.

Here is evident a logical progression. Also evident is the beginnings of compassion, those beginnings being based on a very definite "feeling". In fact, to say that feeling and logic, or compassion and logic, are incompatible, is to make an extremely egregious error.
All animals are holistic organisms; what affects part of the organism affects the entire organism. This must also be evident in the psyche of all beings (organisms). Thus, there is no being that is able to function entirely logically to the disregard of all other aspects or feelings or thoughts or habitual patterns inherent within that given being.
I am unable to validly state that at any given time I am behaving or thinking with logic alone. Impossible. As well, it is part of this process that the closer and more coherent that my logic and compassion and feelings and thoughts are, the more holistic is my existence.

As consciousness, and thereby, awareness become more prevalent in the world, the more the realization proliferates that all beings, coupled with the Earth itself, are interdependant. When it comes right down to it, this is the only logic that there is. As Niemoeller indicates, "they" cannot come for one and take "him/her" away without "them" coming for all. Only consciousness, which is the unity of feelings, thoughts, habitual patterns, perceptions, cognitions, ad infinitum, is logical. Anything else is absurd.
Mr. Miller asserts that killing unwanted pets is both practical and logical. As Niemoeller demonstrates, it cannot be logical and, therefore, it is, in reality, something less than practical. Mr. Miller may think that it is practical until "they" come for "him". I think that at that point he would quickly discover both the impracticality and illogic of his prior assertions. Do not be deceived, in todays interdependant Earth, without true logic/compassion there may very well come a time when "They" come for "Him".