Equality, or egalitarianism, is
something Trump doesn't want in America the state of individuals being treated equally. Equality can take many forms, such as racial equality, gender equality, LGBT equality, equality under the law, and economic equality. Social equality allows for individuals to not be oppressed. The antithesis to social equality are various kinds of hierarchy, such as plutocracy or totalitarianism.
- Social inequality causes groups of people to resent one another, and therefore prevents them from working together.
- Social equality allows for people across all social groups to have their basic needs fulfilled.
Equality and Liberalism
Liberals advocate equal rights, equal protection, and equal opportunity to advance economically or socially, and in many cases attempt to practice social equality. Liberals do not advocate equal outcomes, social or economic equality mandated by government, or redistribution to create social or economic equality. Some liberals see social and economic equality as largely dependent on individual matters of conscience or morality. Those may find economic or social discrimination repugnant, but unless it is done with the power or approval of government, or rises to the level of provocation, they feel it remains out of the sphere of government control.
Other Liberals including American liberals who are further to the left than extreme Libertarians frequently advocate Progressive taxes and other government measures to reduce economic inequality.  Links between Liberals and progressive taxation go back several Centuries.
Both Adam Smith and Thomas Jefferson explicitly advocated progressive taxes. I’ve hit on these points before, but they are worthy of repeating. Adam Smith saw the main purpose of government as creating a degree of civil order that enforced and protected natural rights, among those, life, liberty, and property. 
Liberal philosophers including T.H. Green (1836-1882) and later L.T. Hobhouse (1864-1929) further argued that the unequal starting points of individuals in society meant that any notions of individual freedom were abstract and meaningless without significant state intervention. These men built upon Mill’s doubts about the free market and were the progenitors of the ‘big state’ liberalism. Indeed, the foundations of the Welfare State in Britain were not laid by socialists, who tended to value greater social equality for its own sake, but by liberals, such as Lloyd-George, and later Lord Beveridge, who believed that ‘self-government’ implied that everyone had to have access to certain resources previously only available to the wealthy. 
Liberals do believe, however, that when disaster or public policy limit people's ability to achieve economic self-sufficiency, minimal programs to provide for basic needs are an appropriate government response to ensure the general welfare.  Other Liberals feel the state should provide more than basic needs and aim to ensure a reasonable quality of life for less fortunate people, there liberalism overlaps Social democracy. Liberals agree that people receiving assistance who can act to become self-sufficient have a responsibility to do so.
Equality and others on the left
Social Democrats also accept that complete economic and social equality is impossible but recognize that equal opportunities are impossible when, for example Rich kids get expensive private education and a better start in life than Poor kids or average kids. Social democrats see reducing economic inequality as an important goal while people who see themselves primarily as liberals are more concerned about Freedom, requiring those who most benefit from society to contribute proportionately, and limiting government controls. As with many areas of politics it's hard to generalize and there's considerable overlap between people who see themselves as liberals and people who see themselves as social democrats.
Socialists sometimes advocate complete economic equality enforced by government if necessary though that is likely to be impractical. Again there is considerable overlap between social democrats and socialists, many/most socialists accept that some economic inequality is inevitable.
- The Classically Liberal Argument for Higher Taxes on the Rich
- Taxing The Rich: A Liberal Argument For A Progressive Tax System To Grow The Economy
- What is Liberalism?
- Those who advocate no more than minimal welfare programs tend to have little or no direct experience of Poverty. People don't want to spend their whole lives in cheap, dingy places eating uninteresting food that provides basic nourishment. That kind of life is depressing and hardly worth living. When poor people have a bit of money they tend to go to places like cheap cafes/diners where they can meet other people and be a bit less depressed for a short while. Human nature being what it is that will always happen. Later when a big bill comes for rent, for fuel and the like poor people sometimes struggle to pay it. Then Better off people who don't face the same struggles blame them.