Pre-History:

Agnes (Quincy’s grandmother) was more than a jealous and resentful that unlike the rest of her upper class family she did not get her letter to Hogwarts.  Her first reaction was to blame her tutors.  Then it was to blame her mother.  Then it followed to ruin all the relationships she had within the wizarding world.  Resulting in her to have a rough fall from the grace of being a daughter of a well respected upper class Halfblood. 

Agnes’ fall from grace was so bad that it was obvious she couldn’t function in the wizarding world. Thankfully her family had some business ties to the muggle world so her father Rupert arranged her a marriage to a muggle man.

The marriage worked out as Agnes has maintained the act and Rupert closed business he had connected with the muggle world a few years after the marriage and distanced themselves from the muggle world to ensure that the Smellie family wouldn't be able to try to climb up to the upper class thru that marriage.  As if Rupert's muggle connections had been attempted to be used the status the family had, under a fake name in the muggle world, was partly due to a few illicit memory charms spread over a few generations to gain and maintain that status.

History:

Merritt was an only child and worked besides his father in the family business eventually inheriting it when his father retired. The Smellie family aspired to rise in status even if the attempt made in the marriage of Merritt's parents failed.  When Merritt was contemplating marriage he to hoped to rise in status that way but in the end married Masie Dankworth, a woman he loved also in the middle class.  Still Merritt taught all their children how important appearances were which they all took to heart.  Though Masie contradicted those lessons somewhat by instilling that intelligence was more important than class. 

The family business wasn’t large enough for them all to inherit so his eldest brother Thaddeus was groomed to inherit the business.  Then his next oldest brother Clifford pursued his interests in the area of medicine becoming a muggle surgeon.  With his two older sisters marrying off with Caroline managing to marry a member of the upper class giving her parents a glimpse that the station of the Smellie’s could rise.  Quincy cared more about excitement and education than he did about class.  As he realized rising too high in station, from seeing how boring Caroline’s new associations were, meant that people did less interesting things and talked more.  Though at the same time he knew he wanted to rise as high as he could while maintaining some excitement in life as his parents taught him station was important. 

Of his family Quincy wanted to follow in his brother Clifford’s footsteps and become a surgeon and worked hard in school to achieve the grades needed to.  Clifford was studying under the more antiseptic approach of surgery at Kings College which in Quincy’s mind was more sophisticatedly clean than the surgical carnage that was typical of the time.  To encourage Quincy further Clifford managed to convince others to let Quincy observer a few surgeries Clifford was performing.  His brother Clifford also encouraged his curiosity by letting him occasionally make a few supervised cuts into the bodies of individuals that died at the hospital that Clifford was practicing surgical techniques on. Quincy also got to observer one typical surgery of the day which reminded Quincy more of butcherly than healing in the one amputation of a leg done by another surgeon who had blooded equipment and a bloody apron.  He couldn't believe how the other surgeon basically said it was going to get bloody anyways.  Quincy obviously knew and accepted that surgery was a bloody affair, but the lack of cleanliness was a shock to him after what he’d been listening to his brother say from his schooling.  Plus, in general Quincy likes things to start and end clean - even if sometimes in the middle messes happen.

Quincy went a bit further in practice as he realized Clifford wasn't going to tell him everything.  He could often be found looking at books not only on human anatomy but of the anatomy of small animals.  Which lead him to try to build on what he saw Clifford do when he saw a rat get its tail stuck cutting it in the mouse trap.  An event he treated like something worthy of an amputation of the rats tail which he succeeded to do, but the rat ran away before he could close up the wound.  Even worse his mother caught him and screamed making it so he couldn't even try to catch the rat again or any further rats.  So that left him to sneaking outside where he managed to once dissect frogs he had caught when he had the opportunity to do so uncaught - and usually outside.

Everything changed in a day when he heard about Hogwarts.  Naturally, he didn’t want to go as he had things all planned out how he would follow in Clifford’s footsteps.  To Quincy Hogwarts seemed like some sort of joke he wanted no part of, but he reluctantly accepted it as it was free and probably better than the local school his parents were going to send him to.  As even if they were middle class with him being the fifth child considering the cost of Clifford, Alexandra and Caroline's schooling his parents weren't looking to pay to send another to school.  Especially when school would have still been free for him this term if he'd stayed at home.

Historical Note: Bloody surgical equipment and aprons were typical for the time and study of the antiseptic approach of surgery was not well adopted and slowly gaining traction in England.  (The basis of the cleaning standards today come from Joseph Lister who was a professor at Kings College which is where I'm having Clifford study so this bio makes sense).