I do not believe it considered to do with a persons social status. The poor could graciously offer turtle doves or pigeons. Therefore, the bodily animal could not atone for sin. Since God was lenient in graciously accepting the birds then the lamb was simply a symbol of the atonement of Christ. Christ sacrificial death was sufficient to amply atone for sin going forward to eternity and backward to the garden.
If Christ represent a blemished sacrifice then He could not provide an unqualified substitute for wicked and corrupted creatures. Because He did not suffer corruption, He was undeserving of the curse. If Christ was corrupted then, we would never escape the fierce curse of the law. The value of our apparent inability is dependent upon the unblemished sacrifice. Consequently, our confidence is confirmed by the unblemished sacrifice that proves that His substitution prevents us from offering God anything of our own. If we could willingly offer something then we would subtract from the considerable value of perfect sacrifice in meeting the active and passive requirements of the law. 
We are confident in approaching God by grace because He offered a supreme sacrifice that was acceptable to satisfy God. His complete substitution provided free grace to sinners. Christ unified our lives in satisfaction of the curse in the unblemished sacrifice in favoring us and cursing our opposition.