The first impression is the last impression
With free hosting, the URL or web link that users will have to type to reach your site will be something like awesomecompany.blogspot.com. Not only are such names long, difficult to remember, and prone to being misspelled, they don't look very professional, and do not convey a sense of reliability or trustworthiness. For a more professional portrayal of your website or your online business, it is wise to invest in a domain name and professional hosting that make it clear to visitors that you are serious about what you do.
Needing more resources or services
If your website becomes popular and successful, it is likely that you will want, or need, more resources from your host. More storage space, higher speeds, better uptime, or specific types of software are some of the things you may not be provided with by free web hosting companies.
Further, if you move from free to paid web hosting, you will not be able to send visitors from your old site to your new domain with the paid host. All of the hard work you put into developing your page and online presence will have been for nothing if you have to start from scratch again.
Free web does not allow for the use of custom error pages. These types of pages are used by web servers to show visitors that there has been an error of some sort. As an example, 404 errors are shown when a page is not found on a server. If you are unable to show custom error messages to visitors, they will come to, and then leave, your site confused about what went wrong. Paid hosting companies allow you to provide custom error pages for specific error types.