Mihi non placet odium; concordia autem et bona voluntas omnibus placent.

Because placere works differently from English to like.

In Latin, the thing that is liked is the grammatical subject, and the person who likes it goes in the dative case.

So:

• mihi = to me
• odium = the subject, hatred
• placet = is pleasing

So Mihi non placet odium is literally Hatred is not pleasing to me, which is the Latin way to say I do not like hatred.

If you used ego, that would be nominative I, which does not fit this construction.

That is because Latin is not using the English pattern I like X.

Instead, it uses the pattern X pleases me.

So in Mihi non placet odium:

• odium is nominative singular because it is the subject
• mihi is dative singular because it shows to whom the thing is pleasing

A very common beginner habit is to look for a direct object after placet, but with placere, the thing liked is usually not an object at all; it is the subject.

Because the verb agrees with its subject.

• odium is singular, so the verb is singular: placet
• concordia et bona voluntas are two subjects joined by et, so the verb is plural: placent

So Latin is doing normal subject-verb agreement:

• one thing pleases me → placet
• two things please everyone → placent

For the same reason that the first clause has mihi.

With placent, the people who are pleased are put in the dative case, not the nominative or accusative.

So:

• omnibus = to all / to everyone
• omnes would usually mean all people as a nominative or accusative plural, which would not fit here

In other words:

• concordia autem et bona voluntas omnibus placent
• literally: harmony and goodwill are pleasing to all

Here omnibus means to all people or more naturally to everyone.

It is the dative plural of omnis. Since no noun is written with it, Latin is using it substantively, meaning something like to all persons.

Context tells us that people are meant here, not all things.

So omnibus placent means they please everyone.

Autem usually means however, but, or on the other hand.

It is a postpositive word, which means it usually comes after the first word or phrase of its clause rather than standing first.

So Latin likes:

• concordia autem ...

rather than:

• autem concordia ...

That is very normal Latin word order.

So the sense is something like:

• hatred does not please me; harmony, however, and goodwill please everyone
• or more naturally in English: but harmony and goodwill please everyone

Bona voluntas is an adjective plus a noun:

• bona = good
• voluntas = will, disposition, goodwill

They agree in:

• gender: feminine
• number: singular
• case: nominative

Together they form one subject: goodwill.

Then that subject is joined with concordia by et, which is why the verb becomes plural:

• concordia et bona voluntas ... placent

Because voluntas is a third-declension noun, and its nominative singular naturally ends in -as.

So voluntas is singular, not plural.

This is worth memorizing, because not all Latin singular nouns end the way first- and second-declension nouns do. Third-declension nouns can have a wide variety of nominative singular endings.

Here are the key forms:

• nominative singular: voluntas
• genitive singular: voluntatis

So in this sentence, bona voluntas is one singular noun phrase.

Latin word order is much more flexible than English word order because the endings show the grammatical roles.

So the basic meaning would stay the same in sentences like:

• Odium mihi non placet
• Mihi odium non placet
• Concordia et bona voluntas omnibus placent

However, word order can affect emphasis and style.

In your sentence:

• mihi comes early, which gives some prominence to to me
• autem sits in its usual second position
• the verbs placet and placent come before the subjects in a way that sounds natural in Latin prose

So the order is not random, but it is not as rigid as in English.

Not exactly. Its core idea is to please.

That is why the grammar looks reversed compared with English:

• English: I like harmony
• Latin style: Harmony pleases me

So it is often helpful to remember placet / placent as:

• is pleasing
• are pleasing

If you think of it that way, the cases in the sentence make much more sense.

Because non usually negates the verb or the whole verbal idea.

So:

• Mihi non placet odium = hatred does not please me

Placing non right before placet is a very common and natural position.

Latin can move non around somewhat for emphasis, but here the most straightforward reading is simply that the whole statement is negative: I do not like hatred.