In the fifth chapter of the second book, "The Jackal", Carton is described as a lazy alcoholic attorney who cannot manage to take even the smallest amount of interest in his own life, he'd rather drink it away. "Sydney Carton, idlest and most unpromising of men," Although this may not mean that he is lazy in his work but rather that he is lazy in life because he is too idle to want to do anything with it. Dickens portrays his existence as a supreme waste of life and he takes every opportunity to declare that Carton cares for nothing (apart from drink) and no one. This is until Darnay's first trial when we see that Carton feels something for Miss. Manette. In the chapter following the trial, "The Jackal", Carton and Stryver talk about the trial. This is when Carton initially shows his feelings for Miss.Manette as he refers to her as the "golden-haired girl". When Carton does build up the courage to tell Lucie how he feels about her he is rejected because she loves the gentlemen, Darnay. "Since it is my misfortune, Mr Carton, to have made you more unhappy than you were before you knew me-". For this reason some may develop sympathy for him, or perhaps he deserves this unrequited love. Some may even admire Carton for knowing only to well that he is not good enough for Lucie, "I know very well that you can have no tenderness for me; I ask for none; I am even thankful that it cannot be." However, one could say that this, at least, is expected of him.
Throughout the book, starting form Darnay's first trial, one's admiration for Carton builds. One may have admiration for Carton at Darnay's first trial because he exposed a false witness, Barsad, and Darnay was acquitted of high treason, which saved his life.
However this admiration is limited by the fact that it didn’t really take a genius to do it.
Although in Dickens' time the real Carton was a disgrace in today's society one may perceive Cartons persona of being a cynical drunk with a lack of self-esteem as well as an intellectual and handsome as "cool" to some extent. These personify a man full of character yet an unstable man who can in fact love. A well-known example of this type of person is "Heathcliffe" from "Wuthering Heights".
For those who choose to see the negative side of Carton his death seems merely as an act of giving up. One could say that Stryver's jackal has very little to lose. Never happy and more often than not, causing trouble. In the midst of a promising youth Carton had "followed his father to the grave". This is to say that Carton had, in a sense, died in spirit when his father died. So for Carton physically dying would be less of a sacrifice than it would any other man.
After the first trial Carton studies his own image in the mirror, ""Do you particularly like the man?" he muttered, at his own image;". He then realises that the young Frenchman is everything that he might have been, "he shows what you have fallen away from, and what you might have been!". This implies that Carton is jealous and shows some hostility towards Darnay. However, a jealous man would'nt sacrifice himself, surely he would go after Lucie and leave Darnay to die. Carton couldn't do that because he made a promise to Lucie and he respects her so, "can I use no influence to serve you? Have I no power for good, with you, at all?"
"Let me carry through the rest of my misdirected life, the remembrance that I opened my heart to you"
It is easy to understand why someone would make this claim (the title) because no one likes a drunk with no self-respect who's just throwing away his life. However the fact that he sacrificed his life not only to save Darnay but to keep his promise to Lucie cannot be ignored and for this he deserves some admiration.
I am very much inclined to agree with the statement for that reason, but my thoughts of Carton also conflict with the statement slightly. This is because he cannot have the lady he loves and he is trying to die with some dignity, for this I have a lot of sympathy for him and so, to some extent, I am inclined to like him.