Because Christadelphians are Unitarians, what we have said in response to Unitarians here also applies to them. The purpose of this essay is to draw out a few unique arguments from Christadelphian literature.
From Jesus: God the Son or Son of God? by Fred Pearce: The first few of Pearce's 24 pages are spent quoting scholars who claim there is no teaching of the Trinity in the Bible and claiming that Nicea was what got the ball rolling. In terms of the Bible, the Shema is quoted using the same argument used by Unitarians, assuming "monotheism" to be the same as unitarianism, pointing to places where Jesus calls the Father his God, Heb. 2:17, and pointing as well to passages that speak of Christ's functional subordination (which as shown in the link, is not problematic) and by appeal to Mark 10:18.
Appeal is also made to the human Jesus being called "the Son of God" -- a title indeed applied only to the human Jesus, but making no statement in terms of whether his personal identity preexisted.
The Holy Spirit is dismissed as not being a person with analysis amounting to 2/3 of a page and no response to contrary data.
Analysis of John 1:1, 8:58, and 17:5 repeat Unitarian arguments we have previously covered. Colossians 1:15-18 and Phil. 2:5-8 are dealt with irrespective of Wisdom parallels (which Pearce clearly does not know) rendering the word "firstborn" in terms of something created at a point in time and explaining Phillipians in terms of Christ's earthly life alone. Again, this we have responded to in our response to Unitarianism.
From The Godhead Explained which has no authorial credit. Much is first made of the alleged "confusing" nature of Trinitarianism. No knowledge is shown of Wisdom theology, and there are no new arguments, merely the same ones used by Pearce and by Unitarians we have covered previously.
From Who is Jesus Christ? which also has no authorial credit. In addition to the arguments above, this tract misuses Luke 2:52 the same way Jewish anti-missionary Gerald Sigal does, failing to recognize it as a standard "biographical" transition statement among the ancients. It does not imply a lack of wisdom or favor with God beforehand.
However, the tract does rightly note (in line with the "kenotic emptying" revealed in Phil. 2) that the preexistent Jesus did indeed divest himself of his own knowledge and power.
A unique "spin" is put on Col. 1:16, where Jesus is said to have been the tool to create the heavens and earth. "Heavens" is redefined to refer to the "political" heavens and the "new heavens and new earth." Given the parallel to the Jewish Wisdom tradition, the lack of necessary adjectives (the "heavens" and "earth" in Col. 1:16 are not said to be the "new" or "political" heavens) which offers no refuge for such an exegesis, this redefining is unwarranted.
Also posited is the idea that if this refers to the literal creation, when Christ died, creation should have disintegrated. One would reply that the body of Christ was all that died; the person of Christ certainly did not.
Begging the question, John 6:38, where Christ says he came down from heaven, is dismissed first by noting the reaction of Jesus' audience, many of whom left, and so it is concluded "they know nothing of the theory of a pre-existent Christ". That is actually the point: Jesus WAS teaching something foreign to their ears.
There is a question as to whether Trinitarians are prepared to say that the "Son of Man" was also preexistent. Yes, we are: see here -- "Son of Man" is a heavy divine title; see also our comments on the preexistence of the Son of Man in Judaism.
6:28 is then placed in opposition to 6:32, which speaks of manna as "bread from heaven", asking if manna was manufactured in heaven or whether it was made on earth by the spirit of God. The parallel is illicit, since the manna is not said to "come down" from heaven but is merely "from heaven."
The tract calls the idea of a pre-existent being becoming "an embryo in the womb of a woman" something "embarrassing" but does not explain why it is embarrassing. It would have been indeed to Greek philosophers, who Unitarians and other parties claim was the source of the Trinitarian "apostasy".
The tract also says that "unfortunately" Wisdom is "personified as a woman" which is only a problem for our modern, gender-concerned society. Gender for the ancients was a matter of role, not equipment; Wisdom played a "feminine" role (that of maintainer of the universal "household") and this has no bearing on the masculine incarnation of Jesus as Wisdom (whom, as we note in the article linked atop, claimed to be this Wisdom anyway). Indeed, widows were allowed to assume "male" roles to survive and were considered as "male" in role by others.
Mark Smith in The Origins of Biblical Monotheism adds another salient point: "Attribution of female roles to gods was by no means an Israelite invention."  Even the OT attributes female imagery to Yahweh (Deut. 32:18, Ps. 22:9-10, Is. 46:3, 66:9, 13) as Jesus applies female imagery to himself (as a mother hen over Jerusalem).
Yahweh and other ancient deities were beyond sexuality, but nevertheless expressed themselves in "genderly" ways. The Ugaritic deity Athtar is called in inscriptions both "father" and "mother". The "male" deities Shamash, Istanu, and Gatumdug are called a "mother". Female deities could also be ascribed male qualities. The Christadelphian objection is anachronistic.