Why do the sentences "I have to get a job" and "I need to get a job" mean the same thing if 'have' and 'need' are antonyms?

Solution 1:

Have to is a periphrastic modal idiom. Need is a semi-modal verb. Must is a modal auxiliary verb.

First, have to is an idiom.
Have to is not a usage of the verb have, in any of its senses, though it used to be.

You can tell this because have to is pronounced differently from have two, for instance.

• I have two shovels in the driveway. (have two = /hævtu/, with a /v/)
• I have to shovel in the driveway. (have to = /hæftu/, with an /f/)

This idiom is a periphrastic modal -- an idiomatic construction that means the same as a modal auxiliary verb, in this case, the verb must. So

• I have to get a job = I must get a job.
• This has to be the place = This must be the place.

although have to and must are quite different with negation

• I don't have to get a job ≠ I must not get a job.
• This doesn't have to be the place ≠ This must not be the place.

Second, need is an odd verb in a number of ways; it's called a "semi-modal" verb because it used to be a modal auxiliary verb, but, along with dare, it can now only be used as a modal auxiliary verb

Modal auxiliary verbs
a) must be the first auxiliary in a verb phrase,
b) must be followed by an infinitive without to,
c) never take tense endings, and
d) don't have any non-finite forms (participles, gerunds, or infinitives).

But ... need can only be used this way in a negative context. I.e, it's a Negative Polarity Item (NPI).

• We don't need to consider this further = We need not consider this further.
• We need to consider this further but not *We need consider this further.
  (the second example in each case is the modal usage; the first is not, and
  thus requires Do-Support, present tense marking, and an infinitive with to.)

So need to is just the ordinary usage of an ordinary verb need, which does not mean (though it isn't quite an opposite of) have in its sense of 'possess'. It does, however, mean pretty much the same thing as have to or must; all of them have similar deontic senses meaning 'be obliged to' for one reason or another.

Have to and must also have epistemic senses, dealing with logic and probability; however, need seems not to have an epistemic sense. This may have been lost along with need's syntactic modal superpowers as it slipped from full modal to semimodal over the centuries.

Solution 2:

The meaning of the word "have" differs when used in the two phrases "have to" and "have a". In the phrase "have to", the word "have" acts as a synonym for "need" in the fact that the speaker needs or has to do something. In the phrase "have a", the word "have" is used to show possession or state of being.

Welcome to the illogical world of the English language.

Solution 3:

Idioms are sometimes more than the some of the definitions of their parts.

have to and need to are synonyms, or closely thus with have to more explicitly indicating something obligatory and need to implying necessity without necessarily an imperative obligation.

The difference is subtle and in most cases can be used interchangeably:

I need to/have to go to the bathroom.

Either would be valid and sufficient to explain the need, though have to would imply an urgency (now) where need to would normally imply at an earliest convenience.

Note also this would be considered more adverbial usage than usage as a verb, considering a verb is implied, if not explicitly stated, after need to/have to.

Meanwhile, the verbs need and have imply a direct object.

I need a hammer.
(A hammer is necessary).
I have a hammer.
(A hammer is in my possession).

However, you can also have to have and need to have (Which mean roughly the same thing; see the first part.)