Why does Scripture imply Jesus had siblings if Mary was "ever virgin" per Catholic belief?

The standard answer is that the Greek word adelphos can be translated as "brother", but can also mean "cousin" or having the same national origin.

a brother, whether born of the same two parents or only of the same father or mother having the same national ancestor, belonging to the same people, or countryman any fellow or man a fellow believer, united to another by the bond of affection an associate in employment or office brethren in Christ his brothers by blood all men apostles Christians, as those who are exalted to the same heavenly place -outline-

Catholics understand the word to mean cousins (i.e., having different parents), while members of the Orthodox church understand it to mean "step-brothers," with Joseph having children prior to marrying Mary. Thayer (using Strong) believes the word means neither cousins nor step-brothers but simply brothers (having the same mother but different fathers).

STRONGS NT 80: ἀδελφός ἀδελφός, -οῦ, ὁ (from α copulative and δελφύς, from the same womb; cf. ἀγάστωρ) [from Homer down];

1. a brother (whether born of the same two parents, or only of the same father or the same mother): Matthew 1:2; Matthew 4:18, and often. That 'the brethren of Jesus,' Matthew 12:46, 47 [but WH only in marginal reading]; Matthew 13:55f; Mark 6:3 (in the last two passages also sisters); Luke 8:19; John 2:12; John 7:3; Acts 1:14; Galatians 1:19; 1 Corinthians 9:5, are neither sons of Joseph by a wife married before Mary (which is the account in the Apocryphal Gospels [cf. Thilo, Cod. Apocr. N. T. i. 362f]), nor cousins, the children of Alphæus or Cleophas [i. e. Clopas] -ibid-

Vine understands it this way:

Brother, Brethren, Brotherhood, Brotherly: denotes "a brother, or near kinsman;" in the plural, "a community based on identity of origin or life." It is used of: (1) male children of the same parents, Matt 1:2; 14:3; (2) male descendants of the same parents, Act 7:23, 26; Hbr 7:5; (3) male children of the same mother, Mat 13:55; 1Cr 9:5; Gal 1:19; (4) people of the same nationality, Act 3:17, 22; Rom 9:3. With "men" (aner, "male"), prefixed, it is used in addresses only, Act 2:29, 37, etc.; (5) any man, a neighbor, Luk 10:29; Mat 5:22; 7:3; (6) persons united by a common interest, Mat 5:47; (7) persons united by a common calling, Rev 22:9; (8) mankind, Mat 25:40; Hbr 2:17; (9) the disciples, and so, by implication, all believers, Mat 28:10; Jhn 20:17; (10) believers, apart from sex, Mat 23:8; Act 1:15; Rom 1:13; 1Th 1:4; Rev 19:10 (the word "sisters" is used of believers, only in 1Ti 5:2); (11) believers, with aner, "male," prefixed, and with "or sister" added, 1Cr 7:14 (RV), 15; Jam 2:15, male as distinct from female, Act 1:16; 15:7, 13, but not Act 6:3. * [* From Notes on Thessalonians, by Hogg and Vine, p. 32.] Notes: (1) Associated words are adelphotes, primarily, "a brotherly relation," and so, the community possessed of this relation, "a brotherhood," 1Pe 2:17 (see 5:9, marg.); philadelphos, (phileo, "to love," and adelphos), "fond of one's brethren," 1Pe 3:8; "loving as brethren," RV; philadelphia, "brotherly love," Rom 12:10; 1Th 4:9; Hbr 13:1; "love of the brethren," 1Pe 1:22; 2Pe 1:7, RV; pseudadelphos, "false brethren," 2Cr 11:26; Gal 2:4. (2) In Luk 6:16; Act 1:13, the RV has "son," for AV, "brother." -ibid-

So, many believe the word adelphos may mean not only uterine siblings, but also relatives having the same nationality.

To answer the last question, there may be a contradiction between Catholicism's Tradition and Scripture, but that is not the same as saying the Bible contradicts itself.