Targeting stigmatises the recipients of social spending.  It exaggerates the gap between those who are beneficiaries and those who are not, as well as the gap between those who are 'deserving' beneficiaries and those who are not.
Targeting therefore increases social conflict and differentiation.  It undermines the sense of social cohesion and shared citizenship fostered by universal systems of provision.
Targeting undermines equity between social classes.  For example, many eligible people fail to take up their due, because they may not know their entitlements (and social policy tends toward

not informing them unless asked); or because they wish to avoid stigmatisation; or because they do not have the capacity to deal with the bureaucracy.
Targeting wastes people's time.  It imposes high transaction costs both on recipients and on public servants, especially where the net results of targeting are minute levels of assistance.
Targeting may actually worsen the relative position of those who are poor by creating a two-tier system of provision (private vs public facilities in health and education, for example).
Though often assumed to be cheaper in terms of public expenditure, excessively tight targeting