I almost daily deal with clients who don't have vector versions of their logo because people think that Photoshop is an acceptable tool to design logos; it isn't. I'm including in that, logos that are exported as PFD or EPS from Photoshop.
They may be file formats that are capable of holding vectors but the files exported from Photoshop don't contain complete and proper vectors; they are at best (and not always) vector paths containing raster fills (and any styles, effects etc. will always be raster). What you think is a vector file is at best partially vector. See How to create vector graphics In Photoshop?
Logos should be delivered in a number of formats, especially and essentially a true vector format. See Logo Pack - What should I include?
Let me respond to your points one by one...
These are the arguments in favor of Illustrator and my answers to them:
- It's vector based. Photoshop has shapes and paths.
At the risk of repeating myself; Photoshop shapes and paths are vector containers for raster fills—they simply don't compare. The only part of Photoshop that is vector is the path data, absolutely nothing that you see is a vector (except maybe live type). So any color; fill or stroke or effect or anything else attached to a shape layer in Photoshop is still a raster image.
Again, see How to create vector graphics In Photoshop?
- You can resize freely. if you use Photoshop shapes, you can do the same;
Yes... Inside Photoshop. As soon as you're outside Photoshop you can't; so useless (or at least significant extra work) to anyone who isn't the person creating the logo.
- It's good for printing. Since you can create the file whatever size you need and even use CMYK, it's not an excuse.
Sure, you can use Photoshop for printing. Photoshop isn't vector though so there are a lot of issues to keep in mind; you need to worry about resolution and colors at all stages—you can't quickly resize your A6 flyer to an A0 poster and if you're printer comes back and asks you for a file 3x the resolution you started at, you're probably in trouble.
Working with spot colors (which is essential for a lot of commercial print work) in Photoshop is also significantly harder. You can't just use a spot color, you need to work in multichannel and create channels for you spots.
See Can't apply a Pantone color in Photoshop and linked Q&As.
- Illustrator has artboards. Just like Photoshop (in the latest versions).
Cool. I still use CS6 so don't have artboards in Photoshop. But I don't see what the argument is here; I doubt artboards in Photoshop would/will change my choice of program at all.
- You see pixels when you zoom in Photoshop. I love it, since the pixels won't be there when you save a PDF file with Ps, I feel I have more control over things while I'm capable of adjust pixel by pixel.
If you're working for a digital output, great. Otherwise that makes no sense. There are no pixels in printing so you're giving yourself an unrealistic sense of control where there is none; it is actually the opposite, you're applying an unneeded limitation on yourself.
That "control" is also limited to a single output size (or multiples in scale thereof).
Now, my arguments in favor of Photoshop:
- Much better pen tool and shapes control.
This couldn't be further from the truth. Other than the Pen tool and Shape tools you don't have much more to work with in Photoshop; Illustrator has a myriad of tools and effects that create, distort and work with vectors. Being unfamiliar with or unaware of a tools capabilities does not mean they are inferior; there is a steeper learning curve with Illustrator, but it is vastly superior to Photoshop with its vector capabilities.
- Awesome layers organization (what I hate in Illustrator).
Photoshop and Illustrator layers panels are not comparable; Illustrator show layers and objects, giving you a lot more control. I can't stand Photoshop's layer organization; but that's mostly because I work with Illustrator and rarely use Photoshop and humans like what they are used to.
- Lighter program. Illustrator runs very laggy in my PC (and it has good specs).
True. I rarely have trouble Illustrator, even on my laptop; but that's besides the point. MS Paint is probably less laggy than Photoshop, that doesn't mean it's better suited to logo design.
- I never plan 100% of my arts before I start them. Because of this, I always have to keep both programs open to edit pics in Photoshop and send them Ai.
Great, that's what you should be doing.
- Awesome "Save for web" and "extract assets" functions.
Illustrator has the same (or comparable, not sure about newer versions) "Save for Web" and "Extract Assets" functions. Photoshop has generally been seen as better for digital assets, although that has changed a lot in recent years. That's mostly a matter of personal preference though, so no arguments there.
- Better (really better) clipping mask.
Clipping masks in Photoshop and Illustrator do fundamentally different things. Clipping Masks in Photoshop are more equivalent to Opacity Masks in Illustrator, and Clipping Masks in Illustrator are equivalent to Vector Masks in Photoshop.
In Illustrator you can use any number of shapes in any configuration, all with distinct appearances and attributes as a single opacity mask, whereas you're limited to a single layer in Photoshop; which—in my opinion—makes them vastly superior.
TL;DR — Use each tool for what it was designed for. Illustrator is a vector program; use it to create vectors. Photoshop is an image editor; use it to create and manipulate raster images. You can do some vector-ish stuff in Photoshop and you can do some image manipulation stuff in Illustrator; but you're just limiting yourself to what can be done and setting yourself up for trouble in the long run.
Apologies for the long answer and apologies if this comes across as anything other than sincere; this is something that I deal with every day and it is truly frustrating.