It avoids the risk (to them) of your being reclassified (by the CRA) to be their employee and for them being liable retroactively to pay the employer portion of payroll taxes (plus interest and maybe penalties). You could also demand pay in lieu of notice, vacation pay etc. if you decided to call yourself an employee. You need to talk to a Quebec-based tax accountant familiar with your kind of business about all the ramifications of this.
You should not enter into this too lightly, the paperwork overhead is significant, the T2 returns are designed for professional accountants, not individuals (the guide is 120+ pages), and paying someone to do them for you will probably cost $2K per year minimum, plus you'll have to remit withholding taxes (employer and employee portions) monthly and collect and remit the Quebec version of HST at least quarterly. If you're late on any of the the ~20 payments and filings per year, there are significant penalties, and even if they screw up something (allocations to the wrong year is a popular one) it will take your time to straighten it out. Winding it down will cost more time and probably money.
Edit: Quebec is one of the two provinces (Alberta is the other) where the Feds do not administer the corporate tax returns for the province, so there may be an additional annual filing for the province, with potentially different rules and language. This hassle was eliminated in Ontario years ago. Again, talk to a tax accountant.
Since payments and filings are separate transactions in general, you're looking at roughly one such item per week, but the bulk of the work will be the quarterly and annual ones (eg. T4A summaries, corporate tax return, prov tax return, QST returns).
I can't really think how this would protect you, since you're unlikely to be granted major credit or be able to take on other liabilities without a personal guarantee of some kind, and if you do take on liability then big clients will often insist on proof of adequate insurance (maybe $5M or more).
There can be some compensating advantages, but it's up to your accountant and you to figure out if it is worth it.