Their argument seems to be that: Pigs are strictly forbidden and impure according to the Quran:
أو لحم خنزير فإنه رجس
or the flesh of swine - for indeed it is impure
— Quran 6:145
حرمت عليكم الميتة والدم ولحم الخنزير وما أهل لغير الله به
Prohibited to you are dead animals, blood, the flesh of swine, and that which has been dedicated to other than Allah
— Quran 5:3
So it would be prudent to stay away from anything derived from them, unless there is a clear and unambiguous evidence to the contrary.
Regarding the hadith:
اذا دبغ الاهاب فقد طهر
When the skin is tanned it becomes purified
— Muslim
There is no specific mention of swine, and the general inclusion is debatable:
المشهور عندنا أن جلد الخنزير لا يدخل في الحديث ولا يتناوله العموم
The mashur view near us is that the skin of swine is not included in the hadith, and does not fall into the general principle.
قال أبو عمر : يحتمل أن يكون أراد بهذا القول عموم الجلود المعهود الانتفاع بها ، فأما الخنزير فلم يدخل في المعنى لأنه غير معهود الانتفاع بجلده ، إذ لا تعمل فيه الذكاة
Abu Umar said: It is probable that the implication in the saying is to include those skins whose use is common, and as far as swine is concerned ... it is not included in the meaning since using and benefiting from its skin is not common tradition, nor is the act of slaughtering it.
ودليل آخر وهو ما قاله النضر بن شميل : إن الإهاب جلد البقر والغنم والإبل ، وما عداه فإنما يقال له : جلد لا إهاب
The second argument is which Nazr bin Shumail presented: اهاب is the noun for the skin of cows, sheep and camels, and the skin of other than these is called جلد and not اهاب
— Tafsir Qurtubi
From Hanafi texts, they consider swine to be inherently impure. An impurity itself can not be purified, e.g. blood, urine, faeces etc. can never be purified themselves, though a cloth soiled by them can be purified by washing. Similarly: a pig is itself, wholly and inherently impure, there is nothing that can be removed from it to leave something pure:
وأما الخنزير فلا تلحقه الذكاة ؛ لأنه محرم العين بمنزلة الخمر والدم فلا تعمل فيه الذكاة ، ألا ترى أنه لا يجوز الانتفاع به في حال الحياة والكلب يجوز الانتفاع به في حال الحياة ؟ فليس هو محرم العين ، والله أعلم .
[ This essentially says what I wrote above, swine is not pure when alive, nor permitted to be used ]
— Tafsir Jassas
وكل إهاب دبغ فقد طهر ... إلا جلد الخنزير
skin that is subjected to tanning becomes pure ... except the skin of pigs ...
بخلاف الخنزير لأنه نجس العين إذ الهاء في قوله تعالى: {فَإِنَّهُ رِجْسٌ} [الأنعام: 145] منصرف إليه لقربه
as against a pig, which is impure in itself
(in its essence) because the pronoun in the words of the Exalted, "It is
filth," refers to it
— Hidayah Sharh Bidayat al-Mubtadi ; English Translation
Further references: