Because in the Middle Ages, hospitals were like monasteries.  The sick people (inmates) of hospitals lived a version of the life that monks and nuns lived, and the hospitals themselves were largely owned and operated by monastic institutions.

While the rare "Methodist Hospital" still exists today, in the middle ages, the lion's share of the almshouses, lazar (leper) houses, and hospitals were founded by Saints and Abbots, or under the supervision of monasteries, and were staffed and managed by the monks and nuns who founded them.  Don't believe me?  Take a look at these pages--lists of medieval monastic establishments in England--and take note of all the hospitals.  Lay persons (knights and dukes) might also found and administer hospitals.  In that case, they, too, were acting upon what they felt was a Christian moral obligation to care for the sick.

In the middle ages, piety meant that Christians cared for the sick, taking on the task as a sacred, moral duty.  Because the "leper" and the sick, the poor, the wanderer, the pilgrim, and the insane were beloved of Christ, so they should be beloved of all Christians. Priors and Abbots founded hospitals as part of this sacred duty.

Monastic hospitals were administered by the monastic brethren and staffed with local parish clergy (hired to say mass for, and comfort, the inmates), or monks (who also worked as clergy) or nuns (as administrators, spiritual comforters and caregivers).  The monks, however, often hired servants (workers) to care for the grounds, buildings, and needs of the sick.  This regular staff included cooks, laundresses, and lay brothers and sisters, who served as stewards and proctors and caregivers.   This is similar to how the monastery ran its own establishment, as well as its other properties and charities. 

Just as today, for a business to run, expenditures had to equal income.  Foundations where often started by the donation of a lump sum, and that money was used to build, renovate, and upkeep the hospital.  The money for foundation of a hospital often came from the lay gentry, kings, dukes, knights, or merchants.  The monastery would be the 'owner and administrator' of many of these foundations, though sometimes some powers still sometimes rested with the the king or lay benefactor. Funding for maintaining hospitals came from the community and was raised as alms.  Almsgiving was a sacred moral duty, and alms were provided by kings, lords, yeomen, church congregations, and those on pilgrimage. 

Just as hospitals were supported by almsgiving and founding donations, so were the monasteries themselves.  Though larger monasteries often owned businesses and farmland, and so were financially prosperous, many others relied on funding from the gentry given in endowments, as gifts, or raised from those who traveled on pilgimage.

When it came to medieval hospitals, piety wasn't reserved for the monks and officiating clergy alone. The inmates of hospitals themselves were required to live an imitation of the monastic life.  From the wayfarer who stayed a night or two in the monastic guest-houses, to the "leper," to the aged, those admitted to a bed in a hospital in the middle ages lived a life of prayer.  Until they recovered or expired, they kept all the canonical hours (and were issued fur 'night boots' for the night prayers), attended daily mass, ate communally, spent their time in work and prayer, kept silence, and devoted the remainder of their lives to God as they were able.

All hospitals were staffed with clergy and servants, but not all hospitals employed physicians.  It seems strange to us today, but 'medicine' was different in the middle ages.  Medical treatment came from the many lay women, and monks and nuns, who were skilled with the medicines of their day.  The goal was healing, but cures were often attributed to divine intervention.  Care of the body concentrated on providing rest, food, and comfort.  While the illness was treated as best as could be, it was the care of the soul that was considered of primary importance.  Prayer and piety and application to the saints were thought to be the best chance of healing and cure, and, if cure was an impossibility, then it was of vital importance to prepare of the soul for death.