Source: Ontario Small Claims Court - A Practical Guide (2011), p. 12.
(ii) Cross-examination of the Plaintiff
§1.32 Following the direct examination of the plaintiff, the defendant or his representative may then embark upon an examination of the plaintiff with two principal objectives in mind: either the destruction of the plaintiff's case through plaintiff's admissions or the advancement of the defendant's case, again through admissions. The defendant's examination of the plaintiff is called "cross-examination" or "cross-questioning". The scope of the cross- examination are the issues in the case. The defendant's representative, there- fore, may ask the plaintiff questions that relate to all matters at issue in the proceedings.
Abbreviate Cross Examination to CE. What motivated the choice of 'Cross'?
My guess: In a CE, the witness is not on the questioning lawyer's side, and so the lawyer must ask only questions that elicit a 'Yes/No' answer, to forestall any dodging by the witness. So the 'cross-' apparently suggests antipathy or enmity.