Issues with the question itself

I can't answer the question directly because it contains assumptions that are not correct - this isn't a particularly accurate statement of Christadelphian beliefs.

From the question asked:

The Christadelphians teach that the devil/Satan is not a personal being but an analogy for describing sin.

It focuses on a minor part of the issue and therefore excludes the primary understanding that passages containing the words Devil and Satan should generally just be translated with something like "adversary" and "false accuser".

Summary

Generally these words are understood to be describing the actions of people, and only occasionally as an analogy. Human Nature is adversarial to God - "no man can stand before God and live", "there is none good but God", "In him that is in my flesh dwelleth no good thing", Jesus was "made sin (nature), who knew no sin (transgression)", and the many statements Paul made in Romans show that Human Nature is "adversarial to God".

Transliteration instead of Translation obscures interpretation

The words "Devil" and "Satan" are generally not translated in english translations, instead they transliterate the original Hebrew and Greek words (diabolos and satan) and then add a capital letter to make them into a personal name. There is no intrinsic justification for doing this except to comply with pre-existing ideas.

For proof that this translation is correct, see any good Hebrew or Greek Lexicon: Gesenius, BDB, DCH, BDAG, Thayer... and you will see the basic underlying idea of the words are something like, "adversary" and "false accuser".

It's not "The Satan" as referring to a single Satan/Adversary throughout time... it's "a satan", one of many people, systems, governments, or organisations that are adversaries to God in what they teach, stand for, or do. See https://www.biblestudytools.com/lexicons/hebrew/nas/satan-2.html as an example that uses glosses from Gesenius and BDB (a revision of Gesenius). If you have access to Logos bible software (for example) you can quickly review entries in a wide range of Lexicons and see this is the case. There will also be reference to the theological interpretation that it ALSO refers to a supernatural being... but that is interpretation not translation.

When translating the words literally as above, in the passages concerning the "Devil" and "Satan". The person being referred to generally becomes obvious from the context of the passage itself - sometimes there are disputes over the exact identity, e.g. Satan in Job. If you want to argue for hours, then raise that one in a room full of Christadelphians.

A good example where it's obvious is, the Apostle Peter being a satan (adversary) to Christ. Peter was in that moment an adversary to his Lord. Suggesting to him that he didn't go up to Jerusalem. Peter didn't realise at the time, but he was suggesting Christ avoided going to Jerusalem and the implications of that were that Christ would have avoided being Crucified... going against his Father's will. Clearly Christ was not going to accept this suggestion and asks Peter to "get behind me" or effectively "get out of my way", "don't prevent me from doing what I must do".

Analogy for sin

The question is partly right.

...analogy for describing sin

There is some truth in this part, but definitely as a secondary aspect. Although as with many passages in scripture, sometimes literal things are used in more poetic language in non literal ways. Analogy, metonyms, synonyms, ...

In general terms though Human Nature can be described as being an Adversary to God. Two ways come to mind:

1. "Sin in the flesh" - also described as motions/emotions of sin, the sin dwelling in me (or the dwelling-in-me sin), law in my members (see Romans). Essentially the lusts of the flesh that bring us to sin if we don't attempt to stop them. Only Christ completely succeeded through his whole mortal lifetime, and he is the only one who will.
2. Dying - Which is an integral part of "fallen" Human Nature. By which I mean the state or Mankind after garden of Eden. Going from a state of "Good", to "dying thou shalt die". Death is described as an enemy of God, "The last enemy that shall be destroyed is death" (1 Cor 15:26).

We read in Hebrews,

Heb 2:14 Forasmuch then as the children are partakers of flesh and blood, He [Christ] also Himself likewise took part of the same, that through death He might destroy him that had the power of death — that is, the adversary (devil).

This fits with the reasoning in 1 Cor 15:26 where "death" is described as an enemy. Given the translators didn't deem it necessary to make "enemy" a proper noun, there is no need to make the Hebrew word for "adversary" a proper noun either. There is perhaps a level of personification in these verses, but nothing that requires a supernatural being of any description.

This doesn't take away from the general literal simplicity of many verses, who's meaning becomes obvious when these Hebrew and Greek words are translated literally not just transliterated and made into proper nouns with no justification other than circular reasoning :- Look at these verses that refer to Satan, they show he exists... why is "adversary" turned into a proper noun (Satan) in these verses... because they are talking about Satan.

Defence

This is a bit of a straw man question because the assertion of what Christadelphians teach is not accurate as I've explained above in the first section.

What is their Biblical defense for such a theology?

I've already explained the reasoning for the two aspects of Christadelphian understanding above. As far as the implicit question, "why not understand devil/satan as personal being... or a supernatural being".

Perhaps turn this question on it's head and ask what biblical defence is there for not just simply translating these words? Other than it removes all scriptural basis for a supernatural being borrowed from Pagan theology and appropriated into Roman Christianity as Rome transitioned from a Pagan state religion to a somewhat compromise "Christian" state religion.

By Occam's razor the simplest solution is more likely to be correct - word just means "adversary". I realise there are many different interpretations of "Satan". But I'd suggest the burden of proof is on the far more complicated solution of creating a supernatural being with all sorts of powers and abilities, when the passages themselves just don't require it.

Many years ago I spent several months having weekly discussions with a local Christadelphian couple. The husband was a prominent leader in their congregation. From the notes I took and the literature they gave me, I can provide something of an answer.

"27 - The devil is another name for sin in ourselves and not a separate supernatural being. Christ overcame it by being sinless though of our nature, and can therefore provide us with a covering for our sins (James 1:14-25; Hebrews 2:14; 9:6).

28 - Satan means an adversary and the word is used about things and people who oppose God's will. Even Peter was once called Satan (Matthew 16:23). God can also sometimes act as an adversary against the wicked (Numbers 22:22; 2 Samuel 24:1 - compared with 1 Chronicles 21:1).

29 - Devils (demons) are not supernatural beings. People with mental disorders were said to have 'evil spirits' - which means disordered minds. There is only one God. The supposed devils of heathen religions did not exist. (1 Corinthians 10:20; Acts 17:18 - strange gods = demons; Isaiah 45:5,7.)" Your Bible Reading Notebook from Christadelphians Worldwide, section at end, 'A Summary of Bible Teachings' p63

"Satan - The Bible term 'Satan' means simply 'adversary' and is used of human beings. 1 Sam.29:4; 1 Kings 11:14,23,25; Psa.109:4,20,29; Mt.16:23. Later it came to mean much the same as Devil, i.e. a personification of the influence of sin or evil, individual or political. Lk.13:16; 22:3,31; Ac.26:18; Rom.16:20; 1Cor.7:5; Rev.2:10,13. Sometimes the personification of the Devil or Satan is on a dramatic scale. Job 1; 2; Mt.4; Lk.4; 10:18; Jude 9." A Declaration of the Truth Revealed in the Bible - as distinguishable from the Theology of Christendom set forth in a series of propositions - The Christadelphians, Birmingham, 1967

"The Devil is not (as is commonly supposed) a personal supernatural agent of evil, and in fact there is no such being in existence. The devil is a scriptural manifestation of sin in the flesh in its several phases of manifestation... after the style of metaphor which speaks of wisdom as a woman, riches as mammon and Satan as God of this world, sin as a master, etc." R. Roberts, source missing from photocopy of this quote.

I have another quote from a booklet published by a man who used to be a Christadelphian. He wrote of Bible passages where Jesus cast out demons: "If such creatures were just a superstition of the day that Jesus pandered to because of peoples' ignorance of the 'real' causes of sickness, which is what I had been taught to believe as a Christadelphian, then Jesus was doing nobody a service by not debunking the old wives' fables (1 Tim.4:7) of His time." However, I won't cite source details as this question is looking for Christadelphian reasons for their views, so this author's arguments against their stance are not called for here. It can be said without fear of contradiction, however, that the many Bible texts cited in Christadelphian literature to support their views about Satan are often interpreted differently by those who attach actual existence to such an evil spirit creature. I simply give that last quote to confirm the official belief about Satan that Christadelphians are expected to accept, and an example of one line of argument made for that particular point.

Nor am I giving this answer to defend their beliefs on this point. This answer lists many Bible texts they claim in support of their view, that is all.

The following paragraphs are copied from http://www.religioustolerance.org/chr_delp.htm which in turn cited the page titled "What Christadelphians believe about the Devil" at the Christadelphians's official website (http://www.christadelphian.org.uk/wcb/devil.html)

The Devil is not viewed by Christadelphians as a quasi-deity with magical powers who travels the Earth trying to lure people into sin --as is believed by most conservative Christian groups. Based on Genesis 6:5, Jeremiah 7:21-28, Matthew 15:19, James 1:13-15, and other passages, they stress that "Temptation and hence sin, comes from inside the person, not outside." Satan is viewed as the principle of evil which resides in people and motivates them to sin and rebel against God.

They point out that the words "devil" does not appear in the Hebrew Scriptures (Old Testament). In the New Testament, these terms are sometimes used to translate the Greek word "diabolos" which means a human slanderer or false accuser. Examples are John 6:70, 1 Timothy 3:11, 2 Timothy 3:1-3 and Titus 2:3.

"Satan" in Hebrew and "satanas" in Greek means an opponent or adversary. Examples are: Matthew 16:23 when Peter was considered an adversary because he opposed what Jesus wanted to do at the time. In Acts 5, Sapphira was an adversary.