1) Liberals tend to favor security and social harmony at the expense of individual liberty. One example: liberals favor income redistribution through progressive taxation, to make people more "equal" and more likely to get along - whereas libertarians believe everyone is entitled to the fruits of his/her own labor, even if there are differences in earnings.
2) Liberals prefer centralized power (or a strong, theoretically impartial, father figure, generally a democratically elected government) to regulate the millions of transactions between individuals - or the market - again, with the end goal of social stability. Libertarians are very staunch opponents of strong government involvement in said transactions between individuals, claiming that giving a government a monopoly in enforcing rules is more dangerous and more corrupting than letting individuals or groups of people compete freely.
3) Liberals favor military intervention around the world, to spread their ideals and to solve humanitarian crises (let's not forget that, due to circumstances, the most war-bent US presidents since the 20th century have been leftist Democrats: Woodrow Wilson and WW1, FDR and WW2, Truman with the atomic bomb and the Korean War, Kennedy with the Bay of Pigs and the Cuban Missile Crisis, LBJ with Vietnam, Clinton with Somalia and Serbia, Obama with Libya, Syria, ISIS, etc.) The one exception to this trend was the Bush dynasty. Right-leaning Republicans such as Harding, Coolidge, Hoover, Ford, Nixon, Eisenhower, and even Reagan (despite his rhetoric) have been more wary of using military power to advance US goals. Libertarians even more so oppose a strong offensive military intervention, and prefer a purely defensive foreign policy.
4) Liberals often dislike unchecked free speech (although not in the US), often opposed to offensive speech. Libertarians believe that one of the pillars of a civilized society is for anyone to publicly espouse any belief without any fear of criminal repercussion. (Again, in the US, most people, including liberals, staunchly protect free speech - perhaps a cultural trait, but in most of Europe and the rest of the world, people can get arrested or fined for making certain ideas public).
5) Liberals are wary of freedom of association, with the assumption that one party in a transaction is always exploiting the other - hence the need to regulate agreements (e.g., establishing minimum vacation time in a contract between a private entity and a private individual). This is to protect the supposedly weaker negotiator. Libertarians believe that transactions between consenting individuals or groups should be left free, without interference from a third party.
5) Liberals tend to favor a strong central authority to affect economic outcomes, and pick "winners and losers" within market competition, through anti-monopoly laws, affirmative action, arbitrary taxation and tariffs, etc. Libertarians are wary of giving a strong central authority this power, with the belief that it corrupts the wielder of said authority.
6) Liberals tend to see people as part of various tribes: genders, races, age groups, economic status, and see some as inherently strong and others as inherently weak, intellectually inferior, unable to compete in a free market. Thus, they prefer policies aimed at benefiting the tribe as a whole, at the expense of the individual. Often, they see the tribes as antagonistic toward each other. Libertarians believe in color-blind, gender-blind, etc policies which apply to each individual exactly the same, stemming from the belief that all individuals can find their niche in society, regardless of the natural talents they possess at birth.
In a nutshell, liberals believe a strong central authority (run by their peers) is necessary to steer society to become better and more harmonious. Libertarians believe that individuals are best off left free to achieve their diverse goals, to cooperate uncoerced, and even if the end result is not so equal, society tends to be better off.
Thus, liberals and libertarians have incompatible sets of beliefs, and it makes absolutely no sense to look for any overlap.